Each - Draper Laboratory

The Draper Technology Digest (CSDL-R-3009) is published annually by The Charles Stark Draper 

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E-mail: techdigest@draper.com 

Editor-in-Chief 

Dr. George Schmidt 

Creative Director 

Charya Peou 

Designer 

Pamela Toomey 

Editor 

Beverly Tuzzalino 

Photography Coordinator 

Drew Crete 

Photography 

Jay Couturier 

Copyright © 2007 by The Charles Stark Draper Laboratory, Inc. All rights reserved. 

Front cover photo: 

Improved accuracy of MEMS-based Inertial Navigation System achieved with coordinated gimbal 

movements during operational calibration updates.

Table 

contents 

of 

Letter from the President and CEO, James D. Shields 

Introduction by Vice President, Engineering, Eli Gai 

Papers 

Innovative Indoor Geolocation Using RF Multipath Diversity 

Donald E. Gustafson, John M. Elwell, J. Arnold Soltz 

Engineering MEMS Resonators with Low Thermoelastic Damping 

Amy E. Duwel, Rob N. Candler, Thomas W. Kenny, Mathew Varghese 

Improving Lunar Return Entry Footprints Using Enhanced Skip 

Trajectory Guidance 

Zachary R. Putnam, Robert D. Braun, Sarah H. Bairstow, and Gregory H. Barton 

A Deep Integration Estimator for Urban Ground Navigation 

Dale Landis, Tom Thorvaldsen, Barry Fink, Peter Sherman, Steven Holmes 

Error Sources in In-Plane Silicon Tuning-Fork MEMS Gyroscopes 

Marc S. Weinberg, Anthony Kourepenis 

Model-Based Variational Smoothing and Segmentation 

for Diffusion Tensor Imaging in the Brain 

Mukund N. Desai, David N. Kennedy, Rami S. Mangoubi, et al. 

2006 Published Papers 

Patents 

Patents Introduction 

Multi-gimbaled borehole navigation system 

Patent # 7,093,370 B2 Date Issued: August 22, 2006 

Mitchell L. Hansberry, Michael E. Ash, Richard T. Martorana 

Flexural plate wave sensor 

Patent # 7,109,633 B2 Date Issued: September 19, 2006 

Marc S. Weinberg, Brian Cunningham, Eric M. Hildebrandt 

2006 Patents Issued 

The 2006 Draper Distinguished Performance Awards 

The 2007 Charles Stark Draper Prize 

The 2006 Howard Musoff Student Mentoring Award 

2006 Graduate Research Theses 

2006 Technology Exposition 

2 

3 

4 

14 

24 

34 

42 

56 

70 

75 

76 

79 

82 

83 

84 

86 

87 

88

As Draper’s new president, it is my 

pleasure to introduce this year’s 

edition of The Draper Technology 

Digest. An important element of our 

strategy is to focus on a limited set of critical 

technical capabilities and to maintain our skills 

in these areas at a world-class level. These capabilities 

are: 

• Guidance, navigation, and control. 

• Autonomous air, land, sea, and space 

systems. 

• Reliable, fault-tolerant embedded systems. 

• Miniature, low-power electronic and 

mechanical systems. 

• Large-scale networked systems integration. 

• Biomedical engineering. 

In each of these areas, we strive to be recognized 

as technology leaders through innovative application 

of technology to solve sponsors’ problems. 

Technology leadership also requires that 

our staff share their accomplishments with the 

broader community by publishing, presenting 

at conferences, and serving on advisory boards 

and panels. 

2 Letter from the President and CEO, James D. Shields 

James D. Shields, 

President and CEO 

The Digest supports our efforts to encourage 

publishing by recognizing the authors of the best 

papers that were produced in the previous year. 

It also provides a forum to consolidate in a single 

volume a sampling of the technical accomplishments 

across the range of our critical capabilities. 

The six papers this year cover topics in guidance, 

navigation and control, microelectromechanical 

systems (MEMS), and biomedical engineering. 

All were either published in a refereed journal or 

presented at a prestigious technical conference. 

Each year, during National Engineers Week, Eli 

Gai, our Vice President of Engineering, presents 

an award to the authors of the best technical 

paper published in the prior calendar year. 

Eli also gives awards recognizing the best patent, 

the most effective task leader, and an outstanding 

mentor to students who work at the Laboratory. 

I congratulate the winners of these awards, whose 

accomplishments are described in this issue. 

Draper’s commitment to advanced technical education 

through the Draper Fellows program, where 

Masters and PhD candidates are supported financially 

and academically by allowing them to do their 

thesis research on a Draper project, continued for 

the 34 th consecutive year. We recognize this year’s 

graduates by listing them and their thesis titles.

Eli Gai, 

Vice President, Engineering 

This issue marks the beginning of the second 

decade of the Draper Technology Digest. 

The fundamental purpose of the Digest is 

to recognize the outstanding achievements 

of Draper’s technical staff, as reflected in the papers 

published and patents awarded during the most recent 

calendar year. The Digest also recognizes the important 

mentoring work performed by Draper’s technical 

staff by honoring the recipient of the Howard Musoff 

Student Mentoring Award. This year’s Digest features 

six excellent technical papers highlighting important 

hardware, software, and systems engineering achievements 

in support of our business areas of Space, 

Tactical, and Biomedical Systems. Also featured in 

this year’s Digest are the recipients of the Best Patent 

issued in 2006 and the winner of the Howard Musoff 

Student Mentoring Award for 2006. 

The first paper in this issue by Donald Gustafson, John 

Elwell, and J. Arnold Soltz was selected to receive 

the Vice President’s Award for Best Paper for 2006. 

In this paper, a new approach to indoor geolocation 

in multipath environments based on geometry-based 

modeling is described. Simulation results show that 

this approach significantly improves indoor geolocation 

accuracy. 

The second paper by Amy E. Duwel, Rob N. Chandler, 

Thomas W. Kenny, and Mathew Varghese 

describes new tools to evaluate and optimize microelectromechanical 

system (MEMS) structures for low 

thermoplastic damping. It includes an example that 

illustrates the use of the tools to design devices with 

higher quality (Q) factors, which results in improved 

sensor performance. 

The third paper by Zach Putnam, Robert Braun, Sarah 

Bairstow, and Greg Barton describes modifications of 

the skip trajectory entry guidance used in the Apollo 

Program for use in the planned Crew Exploration 

Vehicle (CEV). A simulation shows that the modified 

guidance significantly improves the entry footprint of 

the CEV for the lunar return mission. 

The fourth paper by Dale Landis, Tom Thorvaldsen, 

Barry Fink, Peter Sherman, and Steven Holmes 

describes optimal estimation techniques used to 

combine a Global Positioning System (GPS)/inertial 

Deep Integration algorithm with measurements from 

other sensors to provide accurate position information 

over extended missions for a personal, wearable 

navigation system. A field test of the system conducted 

under realistic GPS-stressed conditions demonstrates 

the practicality of the design. 

The fifth paper by Marc Weinberg and Tony Kourepenis 

describes the error sources limiting the performance 

of silicon tuning-fork gyroscopes (TFGs) and the techniques 

that can be used to minimize them. The study 

includes three different sensors: the Honeywell/Draper 

TFG, the Systron Donner/BEI quartz sensor, and the 

Analog Device/ADXRS. 

The last paper by Mukund N. Desai, David N. Kennedy, 

Rami S. Mangoubi, Jayant Shah, Clem Karl, Andrew 

Worth, Nikos Makris, and Homer Pien describes the 

application of a unified algorithm to smoothing and 

segmentation of diffusion tensor imaging in the brain. 

Results show improvement in brain image quality both 

qualitatively and quantitatively, as well as the robustness 

of the algorithm in the presence of added noise. 

This year, two patents were selected for the Vice President 

of Engineering’s Award for Best Patent: Multi- 

Gimbaled Borehole Navigation System authored by 

Mitchell Hansberry, Richard Martorana, and the late 

Michael Ash, and Flexural Plate Wave Sensor authored 

by Marc Weinberg, Brian Cunningham, and Eric 

Hildebrant. 

Nine staff members were nominated for the Howard 

Musoff Student Mentoring Award, and the winner 

for 2006 was Laura Forrest. Details on the award and 

Laura’s accomplishments can be found on page 86. 

Introduction by Vice President, Engineering, Eli Gai 3

4 

Innovative Indoor Geolocation 

Using RF Multipath Diversity 

Donald E. Gustafson, John M. Elwell, J. Arnold Soltz 

Copyright © 2006, The Charles Stark Draper Laboratory, Inc. Presented at IEEE PLANS 2006, San Diego, CA, April 25-27, 2006 

Best PaPer 

2006 

abstract 

A new concept is presented for indoor geolocation in 

multipath environments where direct paths are sometimes 

undetectable. In contrast to previous statistically-based 

approaches, the multipath delays are modeled using a 

geometry-based argument. Assuming a series of specular 

reflections off planar surfaces, the model contains a maximum 

of three unknown multipath parameters per path that 

may be estimated when geolocation accuracy is sufficiently 

high. If some of the direct paths subsequently become 

undetectable, it is possible under certain conditions to 

maintain geolocation accuracy using only the indirect path 

length measurements. The new concept is illustrated via 

simulation using a relatively simple representative scenario. 

Performance is compared to a traditional method that uses 

only direct path measurements, indicating the potential 

for significantly improved indoor geolocation accuracy 

in environments dominated by multipath. Since the estimated 

multipath parameters are geometry-dependent, this 

approach allows the possibility of building up indoor map 

information as the geolocation process commences. 

Introduction 

A number of approaches have been suggested for locating 

and tracking people and objects inside buildings where 

Global Positioning System (GPS) operation is denied. 

Most of these use radio frequency (RF) phenomena and 

are limited in performance by a single phenomenon: RF 

multipath. Performance has relied on the ability to determine 

the direct path distance from a number of reference 

sources to the person or object of interest. Within indoor 

environments, the received signal strength of indirect paths 

is often greater than the direct paths, sometimes resulting 

in undetected direct paths and detected indirect paths. [1] 

In these situations, methods based on direct paths cannot 

maintain accurate tracking over a period of time, particularly 

when the object being tracked moves in an unpredictable 

fashion. This limitation can be overcome in some 

cases by exploiting the geolocation information contained 

in the indirect path measurements.

This paper presents a new solution to this problem. Rather 

than treating multipath signals as noise and attempting to 

mitigate multipath-induced errors, this technique exploits 

the multipath signals by using them as additional measurements 

within a nonlinear filter. The nonlinear filter uses 

simultaneous indirect and direct path measurements to 

build up parametric models of all detected indirect paths. 

If one or more direct paths are subsequently lost, the 

nonlinear filter is able to maintain tracking by navigating 

off the indirect path measurements. Previous approaches 

to indirect path length modeling have relied on statistical 

models (e.g., direct-path length plus bias). In contrast, 

our approach is geometry-based. Of importance is the fact 

that the indirect path distance after a sequence of specular 

reflections off planar surfaces can be modeled exactly 

using only two parameters in two dimensions and three 

parameters in three dimensions, for any number of reflections. 

These parameters are estimated in real time in the 

nonlinear filter. 

Problem Formulation 

A typical indoor multipath RF signature is shown in Figure 

1, assuming a bandwidth of 200 MHz. [2] Received signal 

amplitude is plotted vs. time delay. The direct path amplitude 

is below the detection threshold, while the amplitude 

of several indirect paths is higher than threshold. In particular, 

the strongest path is the first indirect path, which 

results in an error of 5.3 m for a geolocation system based 

on direct path measurements. 

Amplitude (mU) 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

Dynamic Range 

Error 

Detection 

Threshold 

Strongest Path 

BW = 200 MHz 

Distance Error = 5.3247 m 

0 

0 20 40 60 80 100 120 140 

Time (ns) 

Figure 1. Typical indoor multipath RF signature. 

Indoor Geolocation System Architecture 

The architecture for the indoor geolocation system under 

consideration is shown in Figure 2. Without loss of generality, 

we consider the problem of tracking a single transponding 

tag. The space is instrumented with multiple RF 

sources at known and fixed locations (nodes). Means are 

available to identify the RF source without error. The signal 

received at a node after reception and retransmission from 

the tag is modeled as 

, 

where z(t) is the transmitted signal, subscript i refers to the i th 

path, (i = 0 is the direct path, and i > 0 is an indirect path), 

a i (t) is the complex attenuation factor, t i (t) is the path 

delay, n(t) is noise, m is the number of indirect paths, and 

t d is the processing delay within the tag, which is assumed 

to be known. The direct path delay is t 0 (t) = ||r(t)-s||/c, 

where r(t) is the tag location, s is the node location, and c 

is the signal propagation speed. 

Received 

Signal 

Preprocessor 

Data 

Association 

Nonlinear 

Filter 

Tag 

Position 

Path 

Delays 

Persistent 

Paths 

Figure 2. Geolocation system architecture. 

The differential delay is the excess delay of the indirect 

path relative to the direct path: 

dt i (t) = t i (t) − t 0 (t) > 0 ; i = 1,2,...,m. 

A preprocessor is used to estimate all detected path delays. A 

number of methods have been developed for this purpose. 

In Reference [3], the received signal was modeled as the 

sum of the direct-path signal and a delayed version (one 

indirect path), with the indirect path amplitude less than 

the direct path amplitude. Using a first-order finite impulse 

response filter model, the differential delay and indirect 

path amplitude were estimated using the autocorrelation 

of the received signal. Another approach [4] used maximum 

likelihood to estimate the direct path delay in a multipath 

environment. In Reference [5], multipath measurements 

were used to increase the accuracy of the direct path delay 

estimate. This method required an a priori statistical model 

of indirect path delay statistics. Differential delays were 

modeled as biases in Reference [6], and algorithms were 

developed for multipath detection and bias estimation. In 

Reference [7], the known autocorrelation function within 

a GPS receiver was used for multipath mitigation. In Reference 

[8], GPS differential delays were estimated using a 

multiple-hypothesis Kalman filter. Differential delays were 

modeled as biases in Reference [9], and a particle filter 

was used for joint estimation of bias and tag location in an 

Innovative Indoor Geolocation Using RF Multipath Diversity 5

indoor environment. The statistical bias model was generated 

using ultra-wideband measurements. 

In practice, it is important to correctly associate each calculated 

delay with the direct path or a specific indirect path 

(i.e., a specific sequence of reflections off the same set of 

reflecting planes). This is not a straightforward process in 

some scenarios with multiple nodes and complex environments 

containing many reflecting surfaces of various 

orientations and size. The problem is made challenging by 

the presence of crossovers between pairs of time delays, 

appearance of new paths, disappearance and reappearance 

of existing paths, and the presence of noise. In order to be 

effective, the data association algorithm should be capable 

of detecting path persistence, so that the largest possible 

number of measurements for each path are obtained; this 

enhances the accuracy of multipath parameter estimation. 

All the methods mentioned above rely on a single parameter, 

the differential delay, for the multipath model. 

Multipath estimation is based on a priori statistical models 

of differential delay, typically as a bias (including means to 

detect sudden bias changes) or output of a low-order linear 

filter. In contrast, the approach suggested here is based on 

a geometrical model and the assumption that the indirect 

path length is the result of a series of specular reflections 

off planar surfaces. This model contains several geometrybased 

parameters and does not depend on a priori statistical 

models of multipath delay. Thus, use of this model allows 

the possibility of inferring geometrical structure within the 

indoor environment. We now develop the measurement 

model that is appropriate for use in a nonlinear filter that 

is capable of joint estimation of tag location and the geometry-based 

multipath parameters. 

Geometry-Based Measurement Model 

In the following, time delays have been converted into 

distances using the known signal propagation velocity in 

air. The indirect path distance after a sequence of m specular 

reflections off planar surfaces is derived as follows. 

Referring to Figure 3, the relevant equations are, for i = 

1,2,...,m 

and 

where p i is the specular point on the i th plane, d 1 is the 

distance from the source to p 1, {d i ; i = 2,3..., m} is the 

6 Innovative Indoor Geolocation Using RF Multipath Diversity 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

distance from p i−1 to p i , d m+1 is the distance from p m to r, w i 

is the unit vector along the incident ray, b i is the distance of 

the plane to the origin of the navigation frame, u i is the unit 

vector normal to the plane, and d is indirect path length. 

From (1), (5), and (6), 

Thus, 

From (3) and (4), 

Thus, 

But, from (1) and (2), 

p 1 

tag r 

w m 

q 1 

q 1 

d m+1 

u m 

d 1 

Figure 3. Geometry for m specular reflections. 

w 2 

u 1 

d m 

q m 

q m 

w m+1 

w 1 

source s 

p m 

(7) 

(8) 

(9) 

(10) 

(11)

Thus 

Continuing, we find that 

(12) 

(13) 

By induction, we see from (8), (12) and (13) that for 

k=1,2,…,m+1 

The case of most interest is k = 1, which gives 

which can be written in the form 

where 

(14) 

(15) 

(16) 

(17) 

is a scalar offset distance that contains contributions from 

all m reflections. In (16), wm+1 is the unit vector from the 

last specular point to the tag and contains potentially useful 

information regarding the geometry of the indoor space. 

The multipath parameters {wm+1 , cm } vary as the tag moves 

through the indoor space. If the variations are too large, 

the parameters may be essentially unobservable, resulting 

in poor performance. Generally, the variations decrease as 

the node moves away from the tag. To see this, write (5) 

in the form 

where 

(18) 

Then 

and 

Since M 1 depends only on the orientation of the reflecting 

planes, w m+1 becomes independent of r as . Similarly, 

from (17), 

so that 

(19) 

Thus, cm also becomes independent of r as . For typical 

indoor environments and tag motion, parameter values 

are generally stable enough to allow reasonable tag localization 

accuracy. A representative example is given in the 

sequel to illustrate this point. An important limiting case 

is the problem of navigation using GPS measurements in 

the presence of multipath. The distance to the nodes (GPS 

satellites) is essentially infinite and the multipath parameters 

are constant over sufficiently short periods of time 

where the effects of satellite motion may be ignored. This 

considerably simplifies the problem of navigating using 

GPS measurements in multipath environments. 

The indirect path parameter set {wm+1, cm} contains three 

unknown parameters in three-dimensional space and two 

unknown parameters in two-dimensional space. Importantly, 

the form of (16) is independent of the number of 

reflections, although the offset distance is significantly 

different. Hence, it does not matter that the number of 

reflections is unknown in practice, and the accuracy of 

estimating {wm+1 , cm } is not affected by the number of 

reflections. For this reason, the reflection subscript m is 

dropped in the sequel. 

Multipath Geolocation system Design 

Equation (16) is in the form of a bilinear measurement 

equation that can be handled using appropriate recursive 

nonlinear filtering methods in which the goal is to track the 

tag location r and estimate the multipath parameters {w, c} 

simultaneously by processing a sequence of noisy measurements 

of d as the tag moves through the indoor space. Note 

that this model includes the unknown effects of additional 

path delays associated with attenuation through materials 

in which the signal propagation speed is slower than in 

air. 

If the parameters are known exactly, then (16) is in the form 

of the usual linear measurement equation for a Kalman 

filter. If the parameter uncertainties are small enough, then 

tag position can be estimated with reasonable accuracy 

using an extended Kalman filter. In some practical situations, 

the uncertainty associated with the initial parameter 


estimates may be large enough to preclude the initial use of 

an extended Kalman filter, and other means (e.g., particle 

filters, multiple-hypothesis filters, information filters) must 

be used at least initially to get within the linear range of an 

extended Kalman filter. 

The form of (16) indicates that accurate estimation of the 

multipath parameters {w, c} depends on meeting several 

conditions: 1) relatively accurate tag location estimates 

over a sufficient length of time, 2) tag motion sufficient to 

ensure observability of the parameters, 3) relatively small 

variation of the of multipath parameters as the tag moves 

through the indoor environment, and 4) persistence of 

the sequence of reflections. In the sequel, it is shown for a 

representative indoor scenario that the parameter variations 

tend to be relatively small as the tag moves through space, 

allowing reasonably accurate estimates of the multipath 

parameters to be obtained. 

Data Association 

A generic measurement data association algorithm is 

depicted in Figure 4. At any time, data for all current and 

past detected indirect paths are stored, both as all past raw 

measurement associated with that path and the coefficients 

of low-order ordinary least squares regression models of 

the path delays. When a new measurement is obtained, 

the distance to all current paths is calculated by comparing 

the predicted values in the current database with the 

new value. If the minimum distance is less than a prespecified 

threshold, then the closest current path is updated, 

including the regression model. If the distance exceeds the 

threshold, a new indirect path is started. Note that new 

indirect paths may be started if a new path appears, an old 

path reappears, or a current path changes by a relatively 

large amount due to tag motion since the last measurement 

of that indirect path. The output of the data association 

algorithm is the identity of the path associated with the 

current measurement. 

Step 1 

Step 2 

New 

measurement 

(y) 

Start new path 

Prediction based on 

OLS path model 

Find distance to current 

closest path 

Figure 4. Generic measurement data association 

algorithm. 


no 

d, k 

d 0 is used in the filter to model the uncertainty 

associated with the unknown control u(i − 1). 

From (16), the indirect path length measurements are 

modeled as 

, 

, 

(22) 

where n(i) is zero-mean Gaussian measurement error. 

Updating at a measurement is performed using the extended 

Kalman filter update equations (cf., Reference [11]) 

where 

(23) 

is the measurement residual and K(i) is the optimal gain 

matrix: 

where 

(24)

and s n(i) is the rms measurement error. 

In case the parameters are assumed to be completely 

unknown initially, it is necessary to initialize the parameter 

estimates and the associated error covariance matrix 

using the first several measurements. This is accomplished 

using the information form of the Kalman filter. [12] Let a 

denote the parameter vector: a T (i) = [w T (i) c(i)] and write 

the measurement equation as 

(25) 

Assume that the first k measurements are direct path 

measurements resulting in accurate estimates of tag position 

and let 

Then, using the recursion, 

the initialization is: 

. 

(26) 

(27) 

(28) 

Direct path measurements are processed using the 

extended Kalman filter equations with x = r, h(x) = 

. 

Estimates of the multipath parameters and covariances are 

unchanged. 

example 

A relatively simple two-dimensional example is presented 

here to demonstrate the potential effectiveness of the 

proposed approach. The performance of two filters was 

compared: 1) the multipath filter, and 2) a conventional 

extended Kalman filter, which operates on direct path 

measurements only. A single RF transponding tag is moving 

within a 30 x 30-m area with planar walls. The initial conditions 

are shown in Figure 5. Two fixed RF nodes at known 

locations are located at adjacent corners of the space. It 

is assumed that the signal attenuation associated with a 

reflection is large enough to preclude detection of signals 

resulting from more than one reflection. Multipath signals 

are thus created by a single specular reflection off either a 

side (East/West) wall or the South wall. A single 5 x 10-m 

rectangular object is located within the room, which blocks 

all RF signals. The geometry in Figure 5 shows the direct 

paths (solid black lines) and the indirect paths (dotted 

black lines) to the transponding tag from the two nodes. 

The two direct paths are unblocked. The two indirect paths 

resulting from reflection off the East and West walls are 

also unblocked; however, the two indirect paths resulting 

from reflection off the South wall are blocked. 

North (m) 

Node 1 Node 2 

30 

25 

20 

15 

10 

5 

0 

x1t0 

0 10 20 30 

East (m) 

Figure 5. Example: initial conditions. 

A particle filter was used initially to reduce the geolocation 

uncertainty to within the linearization region of 

an extended Kalman filter. A total of 25 particles was 

assumed, with the particles initially distributed uniformly 

within the room (black “x” in Figure 5). The initial 1-sigma 

error ellipse is shown by the dotted red circle. Initialization 

was accomplished by sequential processing of one direct 

path measurement from each of the two nodes (solid black 

lines) at the initial time. A standard sequential importance 

sampling algorithm [10] was used, with the normalized 

importance weights proportional to the measurement 

likelihood function. The rms measurement error was s n 

= 1 ft. Since there were relatively few particles and the 

measurement error was much smaller than the initial position 

uncertainty, the first particle filter update yielded 

only two unique particle locations (population = 10 and 

15), an example of the well-known problem of particle 

impoverishment. A simple spreading algorithm was used 

to increase particle diversity. The particles at each location 

were spread by sampling from a Gaussian distribution with 

an rms value of 1.5 m/axis. The same process was followed 

after updating using the measurement from Node 2. 

The results of the initialization procedure are shown in 

Figure 6. Both filters were initialized with the same estimates. 

The particle mean was used to initialize the tag position 

estimates to 

meters, while the tag position error covariance matrices 

were initialized to P(1) = 0.09 I 2 meter 2 , in agreement 

with the assumed rms measurement error. The maximum 

dispersion of any particle from the true tag location was 5.7 

m, so that the dispersion of the particles was reduced to 

the point where initialization of the extended Kalman filter 

could be performed. 


North (m) 

Node 1 Node 2 

30 

25 

20 

15 

10 

5 

0 

x1t1spr 

0 10 20 30 

East (m) 

Figure 6. Conditions after particle filter initialization. 

Available measurements were processed every 0.5 s. Tag 

speed was held constant at 0.5 m/s. No dead reckoning 

sensors were employed, so that the geolocation estimates 

calculated by both filters were not propagated between 

measurements; however, the error covariance matrices 

were increased within both filters using (21). The process 

noise covariance matrix Q(i) = v(i)I was calculated using 

sequential differencing of the position estimates to estimate 

the variance v(i). 

The simulation was run for 94 s at a time step of 0.5 s. 

The time delay (in meters) for the direct and indirect paths 

are plotted in Figure 7. The two indirect paths from Node 

1 have a single crossover point at 20 s. The two indirect 

paths from Node 2 have a single crossover point at 70 s, 

with a near-crossover at 17 s. The data association algorithm 

given in the previous section was employed using 

quadratic regression models and produced no data association 

errors. 

The true and estimated paths over time for both filters 

are shown in Figure 8. True tag location is shown by the 

solid black line. The estimated path for the multipath filter 

(MP) is shown by the solid colored line, while the estimated 

path for the conventional filter (CV) is shown by the 

dotted colored line. While both direct paths are detected 

(for the first 55 s), the MP filter and the CV filter produce 

identical geolocation estimates (blue line). After the direct 

path from Node 2 is lost at 55.5 s, the CV filter is able to 

navigate off the direct path from Node 1 only, while the MP 

filter, in addition, is able to navigate off the indirect path 

from Node 1 reflected off the bottom wall and the indirect 

path from Node 2 reflected off the West wall. The MP 

filter estimate (solid red line) produces very small tracking 

errors, while the CV filter errors (dotted silver line) start to 

grow. When both direct paths become undetected at 73.5 

s, the CV filter can no longer track at all; its geolocation 

estimate remains constant for the remainder of the simulation. 

In comparison, the MP filter is able to navigate off the 


m 

m 

North (m) 

70 

60 

50 

40 

30 

20 

Node 1 

10 

0 20 40 60 80 100 

60 

50 

40 

30 

20 

Time (s) 

x1dy 

10 

0 20 40 60 80 100 

30 

25 

20 

15 

10 

5 

0 

Node 2 

Time (s) 

Figure 7. Measurement delay vs. time. 

Node 1 Node 2 

x1tag 

0 10 20 30 

East (m) 

Figure 8. Comparison of true and estimated paths. 

detected indirect paths. Between 73.5 and 77.5 s, the MP 

filter navigates off the indirect path from Node 1 reflected 

off the bottom wall and both indirect paths from Node 2. 

At 78 s, the indirect path from Node 2 reflected from the 

West wall becomes undetected, and the MP filter is reduced 

to using both indirect path measurements off the bottom 

wall. At 84 s, all four indirect paths become detectable and 

are used by the MP filter until the end of the simulation.

m 

m 

m 

30 

20 

10 

North Position 

0 

0 20 40 60 80 100 

4 

2 

0 

-2 

North Error: MP 

Time (s) 

-4 

0 20 40 60 80 

4 

2 

0 

-2 

North Error: CV 

Time (s) 

-4 

x1npe 

-10 

x1epe 

0 20 40 60 80 

0 20 40 60 80 

Time (s) 

Figure 9. North position tracking performance 

comparison. 

Figures 9 and 10 compare the tracking performance for 

the two filters along North and East. Position estimate 

histories are shown in the top panel. Solid lines show MP 

estimates, while dotted lines show CV estimates; red lines 

begin at 55.5 s, when the direct path from Node z is lost. 

The middle panel displays the error histories for MP, while 

the bottom panel displays the error histories for the CV. 

True errors are indicated by solid lines and filter-derived 

1s error bounds are shown in dotted lines. The red lines 

indicate the performance after the direct path from Node 2 

is lost at 55.5 s. The ability of MP to recover over the last 10 

s, after all four indirect paths are detected, is clearly shown. 

In comparison, CV cannot use the indirect path measurements 

and its geolocation errors continue to diverge. 

Multipath parameter estimation performance is shown in 

Figure 11 for the two indirect paths associated with Node 1 

and in Figure 12 for the two indirect paths associated with 

Node 2. In this two-dimensional example, the multipath 

parameters are the angle y(i) = arctan(x1(i)/x2(i)) (four 

quadrant) and the offset parameter c(i). In the figures, the 

solid black lines denote the true parameter values. The 

blue lines denote the estimates during periods of time 

m 

m 

m 

20 

15 

10 

5 

East Position 

0 

0 20 40 60 80 100 

0 

-5 

-10 

0 

-5 

East Error: MP 

Time (s) 

0 20 40 60 80 

East Error: CV 

Time (s) 

Time (s) 

Figure 10. North position tracking performance 

comparison. 

when the multipath parameters are being estimated (direct 

and indirect path measurements are available simultaneously), 

while the red lines denote the estimates during 

periods when direct path measurements are unavailable. 

PSI (deg) 

Node 1, MPATH #1: PSI 

-50 

-100 

-150 

0 20 40 60 80 

Time (s) 

m 

Node 1, MPATH #1: Offset 

80 

60 

40 

20 

0 

0 20 40 60 80 

Time (s) 

Figure 11. Multipath parameter estimation: Node 1 

measurements. 

Deg 

m 


50 

0 

-50 

0 20 40 60 80 

Time (s) 


80 

60 

40 

20 

0 

0 20 40 60 80 

Time (s) 

x1par1 


PSI (deg) 

m 


150 

100 

50 

0 20 40 60 80 

Time (s) 


80 

60 

40 

20 

0 

0 20 40 60 80 

Time (s) 

Figure 12. Multipath parameter estimation: Node 2 

measurements. 

For Node 1, the parameters for the first indirect path (off 

the West wall) are estimated with reasonable accuracy after 

40 s. The parameters for the second path (off the South 

wall) cannot be estimated for the first 27 s since the indirect 

path is blocked by the rectangular object. When estimation 

commences at 27.5 s, the parameters are almost immediately 

estimated with high accuracy, and this accuracy level 

continues until the direct path is blocked at 73.5 s. 

For Node 2, the parameters for the first indirect path (off 

the East wall) are estimated with reasonable accuracy 

after 45 s. The direct path becomes blocked at 55.5 s, so 

that further updating of the parameter estimates was not 

possible. The second indirect path (off the South wall) 

was blocked for the first 34 s. At 34.5 s, the indirect path 

became unblocked and the indirect path parameters were 

estimated. At the next time step (35 s), the direct path 

became blocked and remained blocked for the remainder 

of the simulation, precluding further estimation of the 

indirect path parameters. Thus, in this case, the indirect 

parameter estimates are based on a single measurement 

pair. 

As discussed previously, the variation in the true multipath 

parameters was relatively small in this representative 

example, so that relatively accurate tag tracking could be 

maintained when it was no longer possible to perform 

parameter estimation. 


deg 

m 


50 

0 

-50 

0 20 40 60 80 

Time (s) 


80 

60 

40 

20 

0 

0 20 40 60 80 

Time (s) 

x1par2 

Conclusion 

A new approach is suggested for the problem of indoor 

geolocation in the presence of dominating multipath using 

RF time-of-arrival measurements. Multipath delays are 

modeled using a geometry-based argument. Assuming a 

series of specular reflections off planar surfaces, the model 

contains a maximum of three unknown multipath parameters 

per path, which may be estimated in a nonlinear 

filter. Simulation results for a relatively simple representative 

example suggest that multipath parameters can be 

estimated with sufficient accuracy to maintain geolocation 

accuracy when one or more direct paths are undetected. 

This approach allows the possibility of building up indoor 

map information as the geolocation process commences. 

references 

[1] Pahlavan, K. and X. Li, “Indoor Geolocation Science and 

Technology,” IEEE Communications Magazine, February 

2002. 

[2] Pahlavan, K., F. Akgul, M. Heidari, and H. Hatami, “Precision 

Indoor Geolocation in the Absence of Direct Path,” submitted 

to IEEE Communications Magazine. 

[3] Moghaddam, P.P., H. Amindavar, R. L. Kirlin, “A New Time- 

Delay Estimation in Multipath,” IEEE Trans. on Signal Processing, 

Vol. 51, No. 5, May 2003, pp. 1129-1142. 

[4] Voltz, P.J. and D. Hernandez, “Maximum Likelihood Time of 

Arrival Estimation for Real-Time Physical Location Tracking 

of 802.11a/g Mobile Stations in Indoor Environments,” IEEE 

Paper No. 0-7803-8416-4/04, 2004. 

[5] Qi, Y., H. Suda, H. Kobayashi, “On Time-of-Arrival Positioning 

in a Multipath Environment,” IEEE Paper No. 0-7803- 

8521-7/04, 2004. 

[6] Giremus, A. and J.-Y. Tourneret, “Joint Detection/Estimation 

of Multipath Effects for the Global Positioning System,” Proc. 

IEEE ICASSP, 2005. 

[7] Do, J.-Y., M. Rabinowitz, P. Enge, “Linear Time-of Arrival Estimation 

in a Multipath Environment by Inverse Correlation 

Method,” Proc. ION Annual Meeting, Cambridge, MA, June 

2005. 

[8] Erickson, J.W., P.S. Maybeck, J.F. Raquet, “Multipath-Adaptive 

GPS/INS Receiver,” IEEE Trans. Aero. Elect. Sys., Vol. 

41, April 2005, pp. 645-657. 

[9] Jourdan, D.B., J.J. Deyst, M.Z. Win, N. Roy, “Monte Carlo 

Localization in Dense Multipath Environments Using UWB 

Ranging,” Proc. IEEE International Conference on Ultra- 

Wideband, Zurich, September 2005, pp. 314-319. 

[10] Ristic, B., S. Arulampalam, N. Gordon, Beyond the Kalman 

Filter, Chapter 3, Artech House, Boston, 2004. 

[11] Jazwinski, A.H., Stochastic Processes and Filtering Theory, 

Academic Press, New York, 1970. 

[12] Bierman, G.J., Factorization Methods for Discrete Sequential 

Estimation, Academic Press, New York, 1977.

(clockwise from left) 

Donald E. Gustafson, 

John M. Elwell and 

J. Arnold Soltz 

bios 

Donald E. Gustafson is a Distinguished 

Member of the Technical 

Staff at Draper with over 40 

years experience in the conceptual 

design and analysis of guidance, 

navigation, and control 

(GN&C) systems. He is one of 

the principal developers of Draper’s 

Deep Integration system for 

GPS-based navigation. Currently, 

he is working on concepts to exploit RF multipath signals in noisy multipath-rich urban and indoor environments for geolocation 

and mapping. Previously, at MIT Lincoln Laboratory, he worked on target surveillance using antenna arrays. Prior to this, he 

was co-founder and Vice President of Scientific Systems, Cambridge, MA, where he worked on aircraft failure detection, adaptive 

control of plastic injection molding machines, biomedical signal processing, meteorological satellite data processing, and 

financial forecasting. At the MIT Instrumentation Laboratory, he worked on Apollo navigation system design and computerized 

electrocardiogram interpretation. He was the co-recipient of two Draper Best Technical Publication Awards, two Draper Patent of 

the Year Awards, and was co-recipient of the 2000 Draper Distinguished Performance Award for the development and demonstration 

of Draper’s GPS/Inertial Navigation System (INS) Deep Integration technique and hardware. He has authored more than 

35 technical papers. He holds a PhD in Instrumentation and Automatic Control from the Massachusetts Institute of Technology 

(MIT) (1973). 

John M. Elwell is a Laboratory Technical Staff Member and is currently Tactical System Program Development Manager with 40 

years experience developing systems for guidance, precision pointing and tracking, and fire control. Recent activity has been in 

the area of long-range guided projectiles for electromagnetic railguns and in the exploitation of RF phenomena in urban environments. 

He is a co-developer of Deep Integration antijam technology for GPS receivers. He has been a member of the Defense 

Science Board Task Forces on Precision Targeting, Missile Defense, and Modeling and Simulation, and has been presented the 

SDIO/AIAA Award for contributions to guidance technology. He has authored numerous papers relating to GN&C and has 

several patents associated with precision pointing and navigation. He holds a BSEE from Northeastern University, an MEE from 

Rensselaer Polytechnic Institute, and an MBA from Canisius College. 

J. Arnold Soltz is a Principal Member of the Technical Staff at Draper with over 40 years experience in the design, implementation, 

and verification of the models of signals, sensors, and systems used for navigation in spacecraft, aircraft, terrestrial surveying, and 

undersea vehicles. Fielded systems have included the integration of inertial navigation technology with GPS, laser tracking, RF 

tracking, and sonar. Recent contributions have included design and development of generalized linear covariance analysis software, 

verification of a model of the indoor RF environment, and the design and verification of a 5-state Kalman filter for removing 

the effects of the ionosphere on GPS signals. He has two Draper patents and was the co-recipient of two Draper Best Technical 

Publication Awards. He has a BA from Johns Hopkins University (1964) and an MS from Northeastern University (1969), and is 

a member of the Institute of Navigation (ION). 


14 

Engineering MEMS Resonators 

with Low Thermoelastic Damping 

Amy E. Duwel, 1 Rob N. Candler, 2 Thomas W. Kenny, 2 Mathew Varghese 1 

Copyright © 2006, IEEE. Published in IEEE JMEMS, Vol. 15, No. 6, 2006 

Nomenclature 

Variable Physical Definition 

E Young’s modulus 

a Coefficient of thermal expansion 

To Nominal average temperature (300 K) 

r Density of solid 

Csp Specific heat capacity of a solid 

Cv Heat capacity of a solid, Cv = rCsp k Thermal conductivity of a solid 

wmech Mechanical resonance frequency 

tn Characteristic time constant for thermal mode n 

s Stress 

e Strain 

l, µ Elastic Lamé parameters 

T Temperature 

S Entropy 

[u v w] Components of displacement in x,y, and z directions, respectively 

= [u, v] 2D vector of mechanical displacements 

Mechanical mode amplitude 

U m 

abstract 

This paper presents two approaches to analyzing and calculating 

thermoelastic damping in micromechanical resonators. The 

first approach solves the fully coupled thermomechanical equations 

that capture the physics of thermoelastic damping in both 

two and three dimensions (2D and 3D) for arbitrary structures. 

The second approach uses the eigenvalues and eigenvectors of 

the uncoupled thermal and mechanical dynamics equations to 

calculate damping. We demonstrate the use of the latter approach 

to identify the thermal modes that contribute most to damping, 

and present an example that illustrates how this information 

may be used to design devices with higher quality factors. Both 

approaches are numerically implemented using a finite-element 

solver (Comsol Multiphysics). We calculate damping in typical 

micromechanical resonator structures using Comsol Multiphysics 

and compare the results with experimental data reported in 

literature for these devices. 

m Mechanical eigenmode shape function 

wm Mechanical resonant frequency for eigenmode m 

An Thermal mode amplitude 

Tn Thermal eigenmode shape function 

wth Characteristic frequency of dominant thermal mode 

DW Energy lost from mechanical resonator system 

W Energy stored in mechanical resonator 

1 Draper Laboratory, Cambridge, MA 

2 Stanford University, Departments of Mechanical and Electrical Engineering, Stanford, CA

Introduction 

Micromechanical resonators are used in a wide variety 

of applications, including inertial sensing, chemical and 

biological sensing, acoustic sensing, and microwave transceivers. 

Despite the distinct design requirements for each 

of these applications, a ubiquitous resonator performance 

parameter emerges. This is the resonator’s Quality factor 

(Q), which describes the mechanical energy damping. In 

all applications, it is important to have design control over 

this parameter, and in most cases, it is invaluable to minimize 

the damping. Over the past decade, both experimental 

and theoretical studies [1]-[6],[9],[22] have highlighted the 

important role of thermoelastic damping (TED) in micromechanical 

resonators. However, the tools available to 

analyze and design around TED in typical micromechanical 

resonators are limited to analytical calculations that 

can be applied to relatively simple mechanical structures. 

These are based on the defining work done by Zener in 

References [7] and [8]. 

Zener developed general expressions for thermoelastic 

damping in vibrating structures, with the specific case 

study of a beam in its fundamental flexural mode. In Reference 

[8], Zener’s calculation was based on fundamental 

thermodynamic expressions for stored mechanical energy, 

work, and thermal energy that used coupled thermalmechanical 

constitutive relations for stress, strain, entropy, 

and temperature. However, in order to evaluate these 

energy expressions for a specific resonator, Zener proposed 

that the strain and temperature solutions from uncoupled 

dynamical equations could be sufficient. He found the 

eigensolutions of the mechanical equation, and, separately, 

the eigensolutions of the uncoupled thermal equation. 

By applying these to the coupled thermodynamic energies, 

Zener calculated the thermoelastic Q of an isotropic 

homogenous resonator to be: 

where the physical constants are listed in the Nomenclature, 

w mech is the mechanical resonance frequency, and t n is the 

characteristic time constant of a given thermal mode. This 

takes into account the fact that multiple thermal modes 

may add to the damping of a single mechanical resonance. 

The contribution of a given mode, n, is determined by its 

weighting function, f n . 

Zener explicitly calculated the weighting functions for a 

simple beam resonating in its fundamental flexural mode. 

In order to make the analysis tractable, he assumed that 

only thermal gradients across the beam width (dimension 

in the direction of the flexing) were significant. This left 

only a 1D thermal equation to solve. Zener found that a 

single thermal mode dominated, giving 

(1) 

(2) 

Few structures are amenable to the simplifications that led 

to expression (2) for Q. However, Zener’s expression (1) is 

quite general. In the section “Weakly Coupled Approach to 

TED Solutions,” we show how numerical solutions to the 

uncoupled mechanical and thermal dynamics of a resonator 

can be used to evaluate (1). This adds a great deal of 

power to Zener’s approach, since arbitrary geometries can 

be considered. 

We show how Zener’s weighting function approach offers 

an intuition into the details of the energy transfer. At the 

same time, our results highlight the limits of intuition in 

identifying the thermal modes of interest. For example, we 

find that the simplification Zener made in assuming only 

thermal gradients in one direction along the beam were 

significant does not capture the most important thermal 

mode, even for a simple beam. In addition, past efforts 

to estimate Q without explicitly calculating the weighting 

functions have been shown [9] to greatly overestimate the 

damping behavior of real systems. This “modified” interpretation 

of Zener’s method can be misleading. 

In this paper, we describe a method for using full numerical 

solutions to evaluate Q using Zener’s approach. We call 

this a “weakly coupled” approach. We also present our 

numerical method for solving the fully coupled thermoelastic 

dynamics equations to calculate Q for an arbitrary 

structure. Using numerical solutions in the weakly coupled 

approach offers powerful guidance in engineering around 

thermoelastic damping, while fully coupled solutions offer 

the ability to precisely evaluate and optimize the thermoelastic 

Q of a resonator. 

Numerical solution of the Fully Coupled teD 

equations 

The coupled equations governing thermoelastic vibrations 

in a solid are derived in Reference [19]. The following 

section, “Governing Equations in 3D,” outlines the basic 

principles of this derivation. “Governing Equations in 2D 

with Plane Stress Approximations” highlights modifications 

required for a 2D plane stress formulation. The full 

2D and 3D equations are written explicitly so that they are 

accessible to the user community. We numerically solve the 

2D and 3D dynamical equations using the finite-elements 

based package Comsol Multiphysics. [11] The Comsol implementation 

is described in References [12] and [13]. This 

analysis can be applied to the wide variety of microelectromechanical 

system (MEMS) resonator structures reported 

in the literature. It is a useful tool for determining whether 

TED limits performance or whether other damping mechanisms, 

such as anchor damping, [23] should be investigated 

instead. “Quality Factor Calculations for Typical MEMS 

Resonators” demonstrates the application of TED simulations 

to a few example MEMS resonator structures. Quality 

factors are calculated and compared with the analytical Eq. 

(1) as well as with experimental measurements reported in 

the literature. 

Engineering MEMS Resonators with Low Thermoelastic Damping 15

Governing Equations in 3D 

The constitutive relations for an isotropic thermoelastic 

solid, derived from thermodynamic energy functions, are 

in matrix form 

and 

where reduced tensor notation has been used, and the variables 

are defined in the Nomenclature. 

To obtain the coupled dynamics, the constitutive relations 

are applied to the force balance constraints and Fourier’s 

law of heat transfer. Force balance in the x direction gives 

with similar relations for the y and z directions. 

Substituting displacement for strain and simplifying, the 

3D equations of motion become 

To obtain the thermal dynamics, we apply Fourier’s law 

The constitutive relations are applied, and the resulting 

equation is linearized around T o , the ambient temperature, 

to give, in 3D 

16 Engineering MEMS Resonators with Low Thermoelastic Damping 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

In summary, Eqs. (6)-(8) and (10) form a set of coupled 

linear equations in 3D. Since the equations are linear, we 

can use a finite-elements-based approach to solving them 

on an arbitrary geometry. We solve for the unforced eigenmodes. 

The generalized eigenvectors contain u, v, w, and 

T at every node. The eigenvalues, w i , are complex. The 

imaginary component represents the mechanical vibration 

frequency, while the real part provides the rate of decay for 

an unforced vibration due to the thermal coupling. The 

quality factor of the resonator is defined as 

(11) 

Governing Equations in 2D with Plane Stress 

Approximations 

For long beams in flexural vibrations, we can identify one 

axis (we chose to be z) in which all strains are uniform 

and no loads are applied. For clarity, we define the x axis 

along the beam length and the y axis in the direction of 

flexing. Along the z direction s 3 , s 4 , and s 5 must be zero 

throughout the structure. This is essentially a plane stress 

approximation. When s 3 = 0 is applied to Eq. (3) above, 

we find that 

(12) 

In the plane stress approximation, the force balance relation 

(5) is 

(13) 

Expanding the stress terms using the constitutive relations 

Applying (12) to (14), the equations of motion become 

The linearized temperature equation is 

(14) 

(15) 

(16) 

(17) 

We apply Eq. (12) and also neglect z-directed temperature 

gradients to obtain

(18) 

In summary, Eqs. (15)-(16) and (18) form a set of coupled 

linear equations in 2D. In order to find Q, we solve for 

the unforced eigenmodes. The generalized eigenvectors 

contain u, v, and T at every node. 

Quality Factor Calculations for Typical MEMS 

Resonators 

The thermoelastic Q values for several example MEMS resonators 

have been calculated. Table 1 introduces the resonator 

structures and the material parameters used. In Table 

2, we summarize the simulated Q values for the various 

structures. We compare simulated results to calculations 

based on Eq. (2) where applicable. We also compare to data 

reported in the literature. In some cases, the experimental 

data appear to have achieved the thermoelastic limit. For 

these devices, it is clear that structural modifications that 

Resonator Units Flexural 

(2D) 

can engineer a higher thermoelastic limit are warranted. In 

devices where the measured Q value is less than half the 

thermoelastic limit, investigation into and minimization of 

other damping mechanisms is warranted. 

A polysilicon beam resonating in its fundamental flexural 

mode was simulated and compared to measurements. [9] In 

the experiments, the beam was actually part of a doubly 

clamped tuning fork to minimize anchor damping. For a 

resonator operating at 0.57 MHz, the measured Q equaled 

10,281. Zener’s formula, Eq. (2), predicts Q = 10,300, for 

the beam at 0.57 MHz and with t = a 2 /p 2 D th (a = 12-µm 

beamwidth in the direction of flexural motion, and D th = 

k/rC sp ). The simulations used only a single clamped beam 

with dimensions matching the beam of the tuning fork. 

The simulated frequency was 0.63 MHz and the simulated 

TED Q = 10,211. This remarkable correlation between 

simulation results and experiments suggests that the flexural 

beam Q is limited by thermoelastic damping. Higher 

thermoelastic Q might be achieved by geometry modifications 

as explored in Reference [9] or by fabricating a given 

structure from different materials as explored in Reference 

[6]. 

Table 1. Summary of Parameters Used in Q Simulation and Calculations for a Longitudinal Resonator. 

Longitudinal 

(2D) 

Longitudinal 

(3D) 

Torsional 

(3D) 

Flexural with 

Slit (3D) 

Material Polysilicon Silicon Si 0.35 Ge 0.65 Silicon Polysilicon 

Material Property References Ref. [9] Refs. [14], [24] Ref. [9] 

Critical Dimensions µm 400 x 12 x 20 290 x 10 x 10 32 x 40 x 2.2 5.5 x 2 x 0.2 150 x 3.5 x 35 

Young’s Modulus GPa 157 180 155 180 157 

Density kg/m 3 2330 2330 4810 2330 2330 

Specific Heat J/kg • K 700 700 377 700 700 

Thermal Conductivity W/m • K 90 130 59 130 90 

Thermal Expansion Coeff. ppm/K 2.6 2.6 4.3 2.6 2.6 

Table 2. Summary of Simulated Q Values for a Selection of MEMS Resonators. Simulation Results Are Compared with 

Calculations Based on Zener’s Single-Mode Approximation and Measured Results Reported in the Literature. 

Fixed-fixed 

beam 2D 

Longitudinal 

2D 

Longitudinal 

3D 

Torsional 

3D 

Fixed-fixed 

beam 2D 

Resonator Simulated 

Frequency 

Measured 

Frequency 

Simulated 

Q 

Analytical 

Q 

Measured 

Q 

Experimental 

Reference 

0.63 MHz 0.57 MHz 10,300 10,300 10,281 Reference [9] 

15.3 MHz 14.7 MHz 1,650,000 N/A 170,000 Reference [20] 

70.5 MHz 74.4 MHz 366,000 N/A 2863 Reference [15] 

4.4 MHz 5.6 MHz 2E8 N/A 3300 Reference [16] 

1.27 MHz 1.15 MHz 26,000 N/A 5600 Reference [21] 


A Si 0.35 Ge 0.65 capacitively-actuated, longitudinal mode 

resonator was modeled and simulated based on geometry 

information provided in Reference [15] and material 

properties reported in References [14], [24]. 4 µm × 

4 µm anchors were included in the simulation, with fixed 

boundary conditions at the ends of the anchors. Quévy et 

al. report the Q measurement of 2863 for the fundamental 

longitudinal mode of a bar resonator. Equation (2) was not 

applied to calculate the analytical Q, since the derivation 

was for flexural modes only. We find that the TED Q is 

two orders higher than the measured Q. This suggests that 

thermoelastic damping, for the fundamental longitudinal 

mode, is not a significant contributor to the overall energy 

loss in this resonator. Other mechanisms, such as anchor 

damping, are being optimized by this group with tangible 

impact on Q being reported. [25] 

A second longitudinal resonator was also simulated. The 

device described in Reference [20] is single-crystal silicon, 

and its resonance length of 290 µm far exceeds its other 

dimensions. This resonator is also capacitively actuated 

and operates at 14.7 MHz. The measured Q is 170,000, 

while the simulated thermoelastic Q is an order of magnitude 

larger. This device also does not appear to be thermoelastically 

limited. 

A paddle resonator operating in its torsional resonance 

was simulated. The simulation model was based on the 

nonmetalized silicon-on-insulator (SOI) device described 

in Reference [16]. Fixed-fixed boundary conditions were 

applied to the ends of the tethers. The simulated resonant 

frequency was about 20% lower than the measured torsional 

frequency. The value of Young’s modulus used in the simulations 

was on the high end of values reported in Reference 

[17], so is unlikely to explain the discrepancy. Analytical 

calculation of the torsional frequency using Reference [18] 

given a total torsional stiffness of 9.4 × 10-12 N • m/rad for 

the beams, and a second moment of inertia of 1.3 × 10-26 kg • m2 for the plate yields 4.3 MHz, within 3% of the 

simulated result. The discrepancy between the measured 

frequency and the theoretical frequencies may be the result 

of fabrication-induced variations in the sample dimensions. 

Evoy et al. reported experimental Q values in the range 

of 3300 for room temperature measurements, while the 

simulations predict thermoelastic Q values of 200 million. 

The simulated result is consistent with the physical understanding 

that torsional deformations produce little or no 

volumetric expansion and should therefore have negligible 

thermoelastic damping. 

Finally, the flexural mode polysilicon beam with a center 

opening described in Reference [21] was simulated. The 

case with a beam length of 150 µm and width of 3.5 µm 

was considered. Since the material parameters of the device 

were not available, we used the polysilicon values of Reference 

[9]. Although the center opening dimensions were 

not provided, the scanning electron microscope (SEM) 

indicated that the slit was extremely narrow. Using Comsol 


Multiphysics, the narrowest slit we were able to model was 

0.1 µm wide, centered in the 3.5-µm beamwidth. The slit 

was also centered in the 35-µm beam height, spaced 2 µm 

from top and bottom. The measured Q was 5600, while 

the simulated TED-limited Q was 26,000. This simulated 

Q dropped to 25,000 for a solid polysilicon beam at the 

same frequency. We also simulated a wider slit and found 

that the Q went up to 26,200 for a slit 0.35 µm wide. This 

suggests that at this frequency, the polysilicon beam has a 

TED-limited Q that starts at 25,000 and can be increased 

with an increasingly wider slit. The experimental reference 

may have had a narrower slit than we were able to 

model, but the simulations were useful in bounding the 

TED-limited Q between approximately 25,000-26,000 

and in identifying the trend. The TED Q is about 4.5 times 

higher than the experimentally measured Q. Though the 

device does not appear to be TED limited, thermoelastic 

damping is clearly important in this device and can still 

be optimized. 

Weakly Coupled approach to teD solutions 

Thermoelastic damping in MEMS resonators can also be 

calculated via a weakly coupled approach proposed by 

Zener. This approach uses eigenvalue solutions to the 

uncoupled mechanical and thermal equations. [8] We show 

how to numerically implement Zener’s approach so that 

structures more complicated than a solid beam can be studied. 

While the fully coupled numerical analysis presented 

in the previous section is much more accurate, we emphasize 

that Zener’s approach can offer design insights that 

might not otherwise be possible. The next four sections 

describe the analysis. For simplicity, the formulas in this 

section are written for the 2D case and use vector notations, 

with 

where u and v are the displacements in the x and y directions, 

respectively. 

In the next section, “Modal Solutions to Thermal and 

Mechanical Systems,” we introduce time-harmonic modal 

expansions for the mechanical and thermal domain solutions. 

Both the thermal modes and the mechanical modes 

of a given structure can be found numerically by eigenvalue 

analysis, assuming no thermoelastic coupling. This 

section also shows how to calculate the relative thermal 

mode amplitudes that are driven by the one mechanical 

mode. The two sections that follow introduce two expressions 

for the energy loss per cycle. In “Energy Lost from 

Mechanical Domain,” the mechanical energy loss as a 

function of mechanical and thermal modes is derived. 

By energy conservation, this is equal to the energy transferred 

to the thermal domain. In “Energy Transferred to 

Thermal Domain,” the energy coupled into the thermal 

domain is taken directly from Reference [8], where the net 

heat rise is derived in terms of the entropy generated per 

cycle. The expressions for energy lost per cycle in these

two sections can be evaluated directly from the modal solutions 

obtained numerically. Although it is not obvious on 

inspection that the two expressions are algebraically identical, 

energy conservation requires that they are equal. We 

have validated this numerically for isotropic solids, and 

Reference [8] provides an algebraic proof for solids with 

cubic symmetry. 

In “Using Weighting Functions to Optimize a UHF Beam 

Resonator,” we apply the weakly coupled formulation to 

the cases of a solid beam and two versions of a slotted 

beam. We describe insights gained by studying the modes 

obtained in the weakly coupled approach. In each example, 

we compare the Q value found with the Q calculated 

through a fully coupled analysis. A thorough experimental 

study of the slotted beam is referenced, [9] where TED 

calculations are compared with experimental measurements 

over a wide range of frequencies. 

Modal Solutions to Thermal and Mechanical Systems 

Zener first identified the mechanical resonant mode of 

interest and assumed a sinusoidal steady state of the form 

(19) 

This is the m th eigensolution to the vector version of Eqs. 

(15)-(16), without the thermal coupling term. (x,y) is a 

real valued modal shape function, U m is the mode amplitude, 

and w m is the mechanical resonant frequency. Note 

that the shape functions and frequencies can be found 

numerically using either Comsol Multiphysics or another 

commercially-available software package. 

Spatial variations of strain caused by the mechanical vibration 

generate thermal gradients that are captured by the 

driven thermal equation 

(20) 

where q c captures the combination of constants written 

explicitly in Eq. (17), and where the term of order a 2 is 

neglected. For simplicity, we also limit our study to one 

mechanical mode at a time, mech and w mech 

(21) 

This equation is solved as a function of the mechanical 

resonance amplitude, U mech . Applying separation of variables, 

the response to a drive at frequency w mech is 

(22) 

The functions T n(x, y) are the real-valued spatial eigenmodes 

of the undriven thermal equation and A n are the 

complex modal amplitudes. To find the modal amplitudes, 

we apply the orthogonality of the eigenmodes T n (x, y). The 

expansion (22) is substituted into (21). Multiplying equation 

(21) by T l and integrating over the volume, we obtain 

with 

(23) 

(24) 

(25) 

The absolute magnitude of |An/Umech| from Eq. (23) can be 

used to assess the effective coupling of mechanical modes 

into the thermal domain. 

To calculate the mechanical quality factor, we first have 

to calculate the energy lost by the mechanical system per 

radian, or equivalently, the energy gained by the thermal 

system per radian. 

Energy Lost from Mechanical Domain 

The energy lost from the mechanical domain per radian is 

(26) 

in 2D, where s 3 = s 4 = s 5 = 0. Stress in the above equation 

is expanded as a function of strain and temperature 

using Eq. (3). The strain is expressed in terms of the modal 

amplitude and shape function. This expansion is further 

simplified by recognizing that only the temperature-dependent 

terms produce nonzero integrals over one cycle. Integration 

over time yields 

(27) 

where each term in this sum, DWn , corresponds to the 

energy dissipated by the nth thermal mode. The thermal 

component of stress that is out of phase with the strain 

damps the vibration, and this term may be identified in the 

first bracket in Eq. (27). The second bracket is the strain. 

Energy Transferred to Thermal Domain 

The expression for energy gained by the thermal domain 

per cycle is derived in Reference [8] to be 

(28) 

The T -1 term is replaced by its Taylor expansion, 1/T 0 − 

T/T o , where it is assumed that the driven modal amplitudes 

are small relative to the ambient temperature. Only the 

latter term in this expansion produces a nonzero integral 

over one cycle, so that 

(29) 


Where k is the thermal conductivity in Joules/(Kelvinsecond-meter). 

Expanding T using (22) and (23), it may 

be shown that Eq. (29) reduces to 


(30) 

Weakly Coupled Quality Factor Calculation 

The maximum stored energy in the 2D mechanical system 

is given by 

(31) 

where the integral is evaluated at the maximum mechanical 

amplitude. This integral may be evaluated directly for 

a given mode shape by substituting Eq. (3) for stress with 

the appropriate 2D approximations (s 3 = s 4 = s 5 = 0). The 

Q of the device is then calculated by 

(32) 

where Qn is an effective Q corresponding to the nth thermal 

mode. In applying Eq. (32) to calculate Q, DW can be 

found from either Eq. (27), the expression for mechanical 

energy lost, or Eq. (30), the thermal energy gained. These 

expressions can be shown to be equivalent. 

This analysis shows that we can use numerically calculated 

modal solutions of uncoupled thermal and mechanical 

equations to calculate the Q. For simplicity, we restricted 

our analysis to a single mechanical mode of interest. We 

considered that possibly many thermal modes would 

contribute to damping in the system. The individual terms 

in the sum Eq. (32) for Q can be used to identify the thermal 

modes that contribute most to damping and evaluate 

their relative weights. 

Using Weighting Functions to Optimize a UHF Beam 

Resonator 

Figure 1 shows the calculated Q values for a range of thermal 

modes in a beam. The beam is assumed to be in its 

fundamental flexural resonance at frequency 0.63 MHz. 

The frequency and mode shape were found numerically. 

The first 40 thermal modes were also found numerically. 

Using the approach described in the previous four sections, 

we evaluated the thermoelastic damping associated with 

each mode. The Comsol Multiphysics module was used 

to evaluate the overlap integrals in |An | (Eq. (23)) that are 

needed to evaluate DW in Eq. (27) or (30). The total Q, 

based on 40 modes in Eq. (32), was found to be 10,400. 

The Q calculated in a full TED simulation as described in 

“Governing Equations in 2D with Plane Stress Approximations” 

was 10,200. The weakly coupled calculations show 

that this damping is dominated by the contribution of a 

single mode, whose thermal eigenfunction is shown in the 

inset. This mode at 0.605 MHz gave Q = 11,000. Interestingly, 

the temperature distribution of this mode is not 

uniform along the beam axis. Although Zener’s original 

approximation assumed that dominant thermal mode had 

no variation along the beam axis, we find that the uniform 

mode, also shown in Figure 1, has a high Q = 6,250,000. 

Q -1 (x10 4) 

1 

0.8 

0.6 

0.4 

0.2 

0.605-MHz Thermal Mode: 

Q = 11,000 

0.60-MHz Thermal Mode: 

Q = 6,250,000 

f mech = 0.63 MHz 

Q tot = 10,400 

0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

Figure 1. Q values for thermal modes in a fixed-fixed, 

thermally-insulated beam that is 400 µm long 

and 12 µm wide. The mechanical resonance is 

the fundamental flexural mode at 0.63 MHz. 

The first 40 thermal modes are calculated. 

The three most heavily damped modes are: 

at 0.6 MHz with a Q of 6,250,000, at 0.605 

MHz with a Q of 11,000, and at 0.611 MHz 

with a Q of 280,000 (spatial profile not shown 

in inset). The total device Q, including all 40 

thermal modes is 10,400. 

After observing the thermal distribution of the dominant 

thermal mode, we consider the effect of placing slots in 

the beam. The slots, proposed originally in Reference [9], 

are designed to alter the dominant thermal mode without 

significant effect on the fundamental flexural mode 

frequency. Figure 2 shows the Qn values for the solid beam 

from Figure 1 next to the results for a slotted beam. The 

slots had the effect of modifying the thermal eigensolutions 

and characteristic frequencies. In the slotted beam, many 

more thermal modes contribute to the damping of the 

structure. On the other hand, the thermal modes with the 

greatest spatial overlap are moved to much higher frequencies, 

minimizing their overall effect on damping. In this 

beam, the slots had the effect of raising the total Q value by 

a significant factor of four. 

If the mechanical mode frequency were already much 

higher than the dominant thermal mode, then moving the 

dominant modes up in frequency could have a detrimental 

effect on Q. This case is shown in Figure 3. Originally, in 

the solid beam, the mechanical frequency is at 4.327 MHz, 

while the dominant thermal mode is still at 0.605 MHz. 

When slots are added to this beam, thermal modes with 

significant spatial overlap move up in frequency, much 

nearer to the mechanical resonance. This lowers the Q to 

20,200 from 38,000 without slots.

Q -1 (x10 4) 

Q -1 (x10 6) 

1 

0.8 

0.6 

0.4 

0.2 

3 

2 

1 

0 

0 1 2 3 4 5 6 

Frequency (MHz) 



and 12 µm wide. The top plot shows the solid 

beam thermal modes and mechanical resonance, 

while the bottom plot shows the same beam 

with 1-µm wide slits along the beam length. 

The effect of the slits on the thermal modes and 

their Q values indicated. The mechanical resonance 

shifts slightly, as expected. The total Q 

value is higher in the beam with slits. 

Q -1 (x10 5) 

Q -1 (x10 5) 

2.5 

2 

1.5 

1 

0.5 


Q tot = 10,400 


Q tot = 40,000 

f mech = 4,327 MHz 

Q tot = 38,000 

400-µm Beam 

Solid Silicon 

400-µm Beam 

Silicon, Slotted 

150-µm Beam 

Solid Silicon 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

fmech = 3.75 MHz 

Qtot = 20,200 

150-µm Beam 

Silicon, Slotted 

0 

0 2 4 6 8 10 12 14 16 

Frequency (MHz) 



and 12 µm wide. The top plot shows the solid 

beam thermal modes and mechanical resonance, 

while the bottom plot shows the same beam 

with 1-µm wide slits along the beam length. 

The effect of the slits on the thermal modes and 

their Q values indicated. The mechanical resonance 

shifts slightly, as expected. The total Q 

value is lower in the beam with slits. 

Since it is not always possible to predict the most relevant 

thermal mode and its time constant intuitively, the 

numerical approach can be extremely helpful. We see that 

simple modifications to the resonator can have the effect 

of completely altering the thermal mode structure and 

introducing complicated weightings in the Q calculation. 

Both the frequency and the spatial overlap of the thermal 

modes are clearly important. When modes that have high 

spatial overlap are also close to the mechanical resonance 

frequency, large thermoelastic damping results. Since structural 

modifications that have a beneficial impact in some 

frequency regimes can be detrimental in others, engineering 

to optimize Q can be greatly enabled through the use 

of the numerical approach described here. 

Conclusion 

This paper presented two new tools to evaluate and optimize 

MEMS structures for low thermoelastic damping. 

The weakly coupled approach is based on original work 

by Zener. We reviewed Zener’s approach and showed how 

numerical finite-elements-based approaches can be used 

to fully leverage Zener’s theory. In the weakly coupled 

approach, the fundamental thermodynamic energy expressions 

are coupled. However, the strain and temperature 

solutions used to evaluate these energies are taken from 

solutions to uncoupled, standard mechanical and thermal 

equations. This allows us to use readily available finiteelement 

packages and evaluate thermoelastic damping. 

The approach enables a great deal of insight into the energy 

loss mechanism. We find that a spatial overlap of thermal 

modes with the strain profile in the mechanical mode of 

interest is a dominant term in the damping. In addition, 

the frequency separation between relevant thermal modes 

and the mechanical resonance frequency must be considered. 

By studying the damping contributions of individual 

thermal modes, their mode shapes, and their frequencies, 

it is possible to engineer MEMS resonators for higher Q. In 

addition, by reviewing the fundamental coupled thermodynamic 

energy expressions, we achieve a greater insight 

into the energy loss mechanism itself. 

Finally, this paper outlines a method for solving the fully 

coupled thermoelastic dynamics to obtain exact expressions 

for Q in an arbitrary resonator. The fully coupled 

simulations enable a precise evaluation of Q. We derive 

both 3D equations, as well as 2D plane stress thermoelastic 

equations. The simulations were conducted in Comsol 

Multiphysics. This software can parameterize the material 

parameters and geometry, so that detailed optimization 

studies are enabled. We showed that the fully coupled 

simulations predict thermoelastically limited Q in structures 

reported in the literature. 

acknowledgments 

The authors would like to thank Mark Mescher and Ed 

Carlen at Draper Laboratory, as well as Saurabh Chandorkar 

and Professor Ken Goodson at Stanford University 

for valuable conversations. We also thank Neil Barbour 

and John McElroy for support at Draper. This work was 

supported by DARPA HERMIT (ONR N66001-03-1-8942). 

The authors thank Dr. Clark Nguyen for his support of this 

portion of the project. 


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Thermoelastic Internal Friction,” Physical Review, Vol. 53, 

1938, p. 90. 

[9] Candler, R.N., M. Hopcroft, W.-T. Park, S.A. Chandorkar, G. 

Yama, K.E. Goodson, M. Varghese, A. Duwel, A. Partridge, 

M. Lutz, and T. W. Kenny, “Reduction in Thermoelastic Dissipation 

in Micromechanical Resonators by Disruption of 

Heat Transport,” Proceedings of Solid State Sensors and Actuators, 

2004, pp. 45-48. 

[10] Nowick, A.S. and B.S. Berry, Analastic Relaxation in Crystalline 

Solids, Chapter 17, Academic Press, New York, 1972. 

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http://www.comsol.com. 

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in MEMS, Master of Science Thesis, Department of Materials 

Science, Massachusetts Institute of Technology, 2002. 

[13] Antkowiak, B., J.P. Gorman, M. Varghese, D.J.D Carter, A. 

Duwel, “Design of a High Q Low Impedance, GHz-Range 

Piezoelectric Resonator,” Proc. Transducers, Solid-State Sensors, 

Actuators and Microsystems, 12 th International Conference, 

2003. 


[14] Schaffler F., Properties of Advanced Semiconductor Materials 

GaN, AlN, InN, BN, SiC, SiGe, M.E. Levinshtein, S.L. Rumyantsev, 

M.S. Shur, Eds., John Wiley & Sons, Inc., New York, 

2001, pp. 149-188. 

[15] Quévy, E.P., S.A. Bhave, H. Takeuchi, T-J. King, R.T. Howe, 

“Poly-SiGe High Frequency Resonators Based on Lithographic 

Definition of Nano-Gap Lateral Transducers,” Proceedings 

of Solid State Sensors and Actuators, 2004, pp. 360-363. 

[16] Evoy, S., A. Olkhovets, L. Sekaric, J.M. Parpia, H.G. Craighead, 

D.W. Carr, “Temperature-Dependent Internal Friction 

in Silicon Nanoelectromechanical Systems,” Applied Physics 

Letters, Vol. 77, No. 15, 2000, pp. 2397-2399. 

[17] http://www.memsnet.org 

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[20] Mattilia, T., A. Oja, H. Seppä, O. Jaakkola, J. Kiihamäki, H. 

Kattelus, M. Koskenvuori, P. Rantakari, J. Tittonen, “Micromechanical 

Bulk Acoustic Wave Resonator,” IEEE Ultrasonics 

Symposium, 2002, p. 945. 

[21] Abdolvand, R., G. Ho, A. Erbil, F. Ayazi, “Thermoelastic 

Damping in Trench-Refilled Polysilicon Resonators,” Proc. 

Transducers, Solid-State Sensors, Actuators and Microsystems, 

12 th International Conference, 2003. 

[22] Ayazi, H., “Thermoelastic Damping in Flexural Mode Ring 

Gyroscopes,” 2005 ASME, November 5-11, 2005, Orlando, 

FL. 

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Anchor Loss Simulation,” Int. Journal for Numerical Methods 

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818. 

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Pisano,T-J. King, and R.T. Howe, “Poly-Sige: a High-Q Structural 

Material for Integrated RF MEMS,” Solid-State Sensor, 

Actuator and Microsystems Workshop, Hilton Head Island, 

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and R.T. Howe, “Anchor Loss Simulation in Resonators,” 

18 th IEEE Microelectromechanical Systems Conference 

(MEMS-05), Miami, Florida, January 30 - February 3, 

2005.

(l-r) Amy E. Duwel and 

Mathew Varghese 

bios 

Amy E. Duwel is currently the 

MEMS Group Leader at Draper 

Laboratory and a Principal 

Member of the Technical Staff. 

Her technical interests focus on 

microscale energy transport and 

on the dynamics of MEMS resonators 

in applications as inertial sensors, RF filters, and chemical detectors. She received a BA in Physics from the Johns 

Hopkins University, Baltimore, MD (1993) and MS and PhD degrees (1995 and 1999, respectively) in Electrical Engineering 

and Computer Science from MIT, Cambridge. 

Rob N. Candler is a Senior Research Engineer at the Robert Bosch Research and Technology Center. His research has focused 

on wafer-level packaging of silicon resonators and inertial sensors and energy dissipation in resonators. He is currently working 

on fundamental limitations of MEMS devices under the DARPA Science and Technology Fundamentals Program. He 

received a BS in Electrical Engineering from Auburn (2000) and MS and PhD degrees in Electrical Engineering from Stanford 

University (2004 and 2006, respectively). 

Thomas W. Kenny was with the NASA Jet Propulsion Laboratory from 1989 to 1993, where his research focused on the 

development of electron-tunneling high-resolution microsensors. In 1994, he joined the Mechanical Engineering Department 

at Stanford University, Stanford, CA, where he directs MEMS-based research in a variety of areas including resonators, 

wafer-scale packaging, cantilever beam force sensors, microfluidics, and novel fabrication techniques for micromechanical 

structures. He is a founder and CTO of Cooligy, a microfluidics chip cooling components manufacturer, and founder and 

board member of SiTime, a developer of CMOS timing references using MEMS resonators. He has authored and coauthored 

more than 200 scientific papers and holds 40 patents. He is currently the Stanford Bosch Faculty Development Scholar and 

the General Chairman of the 2006 Hilton Head Solid-State Sensor, Actuator, and Microsystems Workshop. He received a BS 

in Physics from the University of Minnesota (1983) and MS and PhD degrees in Physics from the University of California, 

Berkeley (1987 and 1989, respectively). 

Mathew Varghese was head of the Microsystems Integration Group and was a Principal Member of Technical Staff at Draper 

Laboratory. His research interests focused on the fabrication, design, and analysis of microsystems. He led projects to build 

microphones, drug delivery devices, MEMS RF filters, and Chip Scale Atomic Clocks (CSAC). Dr. Varghese won a Distinguished 

Performance award for leading the CSAC development effort at Draper. He received a BS in Electrical Engineering 

and Computer Science with a minor in Physics from the University of California, Berkeley, and SM and PhD degrees in 

Electrical Engineering and Computer Science from MIT (1997 and 2001, respectively). 


24 

Improving Lunar Return Entry 

Footprints Using Enhanced Skip 

Trajectory Guidance 

Zachary R. Putnam, 1 Robert D. Braun, 2 Sarah H. Bairstow, 3 and Gregory H. Barton 4 

Copyright © 2006 The Charles Stark Draper Laboratory, Inc. Presented at Space 2006 Conference, San Jose, CA, 

September 19-21, 2006. Sponsored by AIAA 

abstract 

The impending development of NASA’s Crew Exploration 

Vehicle (CEV) will require a new entry guidance algorithm 

that provides sufficient performance to meet all requirements. 

This study examined the effects on entry footprints 

of enhancing the skip trajectory entry guidance used in the 

Apollo program. The skip trajectory entry guidance was 

modified to include a numerical predictor-corrector phase 

during the atmospheric skip portion of the entry trajectory. 

Four degree-of-freedom (DOF) simulation was used to 

determine the footprint of the entry vehicle for the baseline 

Apollo entry guidance and predictor-corrector enhanced 

guidance with both high and low lofting at several lunar 

return entry conditions. The results show that the predictor-corrector 

guidance modification significantly improves 

the entry footprint of the CEV for the lunar return mission. 

The performance provided by the enhanced algorithm is 

likely to meet the entry range requirements for the CEV. 

Introduction 

In 2004, the President of the United States fundamentally 

shifted the priorities of America’s civil space 

program with the Vision for Space Exploration (VSE), 

calling for long-term human exploration of the Moon, 

Mars, and beyond. [1] This program focuses on returning 

astronauts to the Moon by 2020 with the eventual 

establishment of a permanent manned station there. 

Experience gained from human exploration of the 

Moon is then to be used to prepare for a human mission 

to Mars. To complete these tasks, a new human exploration 

vehicle, the Crew Exploration Vehicle (CEV), will 

be developed. 

1 Graduate Research Assistant, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA. 

2 Associate Professor, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA. 

3 Draper Fellow, Mission Design and Analysis, Draper Laboratory. 

4 Group Leader, Mission Design and Analysis, Draper Laboratory.

The NASA Exploration Systems Architecture Study 

(ESAS) selected a CEV similar to the Apollo program’s 

Command and Service Module, with a crewed 

command module and uncrewed service module. [2] The 

CEV command module will be a scaled version of the 

Apollo Command Module (CM), maintaining the same 

outer moldline with a larger radius. In addition, the 

CEV will be required to return safely to land locations 

during normal operations, as opposed to the ocean 

landings performed in the Apollo program. Successful 

land recovery operations require an entry guidance 

algorithm capable of providing accurate landings over 

a large capability footprint. Preliminary requirements 

indicate that the CEV entry vehicle must be capable of 

downranges of at least 10000 km. [3] 

The Apollo program entry guidance contained a longrange 

option to provide an abort mode in the event of 

poor weather conditions at the primary landing site. 

A long-range entry capability also simplifies the phasing 

and targeting problem by allowing the vehicle to 

perform entry targeting within the atmosphere during 

entry, possibly saving propellant during in-space entry 

targeting. Long-range entries can be achieved easily by 

moderate lift-to-drag ratio (L/D) blunt body entry vehicles, 

such as the CEV, by employing a skipping entry 

trajectory. When performing a skipping entry, the vehicle 

enters the atmosphere and begins to decelerate. The 

vehicle then uses aerodynamic forces to execute a pullup 

maneuver, lofting the vehicle to higher altitudes, 

possibly exiting the atmosphere. However, enough 

energy is dissipated during the first atmospheric flight 

segment to ensure that the vehicle will enter the atmosphere 

a second time at a point significantly farther 

downrange than the initial entry point. After the second 

entry, the vehicle proceeds to the surface. A longer 

range trajectory is achieved in this manner, as shown 

in Figure 1. 

Attitude (km) 

125 

100 

75 

50 

25 

0 

No Skip Entry 

Skipping Entry 

0 500 1000 1500 2000 

Time (s) 

Figure 1. Skipping and nonskipping entry trajectories (altitude 

vs. time). 

The Apollo CM was capable of a maximum entry downrange 

without dispersions of 4630 km (2500 nmi) 

when employing the Kepler (ballistic) phase of its skip 

trajectory guidance. [4 ] However, this capability was 

never utilized. Studies for the First Lunar Outpost in 

the early 1990s used a 1.05 scale Apollo CM. These 

studies also employed the Apollo entry guidance algorithm 

and found a similar maximum downrange without 

dispersions of 4445 km (2400 nmi). [5] However, 

in this study, trajectories using the Kepler phase of the 

guidance were excluded from nominal trajectory design 

for the following reasons: 

(1) Desire to maintain aerodynamic control of the vehicle 

throughout entry. 

(2) Relative difficulty of accurate manual control 

to long-range targets in the event of a guidance 

failure. 

(3) Sensitivity to uncertainty at atmospheric interface 

and within the atmosphere, leading to inaccurate 

landings. 

(4) No operational necessity for long-range entries. [5] 

While these issues remain significant concerns for the 

design of the CEV entry system, preliminary requirements 

state that the CEV must be able to achieve a downrange 

of at least 10,000 km. Recent analyses indicate 

that the moldline of the CEV is fully capable of achieving 

downranges of this magnitude. [6] However, significant 

enhancements in the Apollo algorithm are required 

to maintain landed accuracy at these downranges. 

Method 

The entry footprint of the CEV entry vehicle was evaluated 

with a 4-DOF simulation written in Matlab and 

Simulink. Entry trajectories were simulated over a 

range of flight path angles, crossrange and downrange 

commands using the baseline Apollo skip trajectory 

guidance and both high and low lofting predictorcorrector 

enhanced entry guidance algorithms. Uncertainty 

analysis was not included in this feasibility 

study. 

Definitions 

This study utilized the following definitions. Atmospheric 

interface, the altitude at which the entry vehicle 

enters the sensible atmosphere, was defined to be 122 

km (400,000 ft) above the Earth’s reference ellipsoid. 

Flight path angle (FPA) refers to the entry vehicle’s inertial 

flight path angle at atmospheric interface. The inertial 

flight path angle is the angle between the vehicle’s 

velocity vector and the local horizontal, where negative 

values refer to angles below the horizon. Downrange 

is defined as the in-plane distance traveled by the 

Improving Lunar Return Entry Footprints Using Enhanced Skip Trajectory Guidance 25

vehicle from atmospheric interface to landing. Crossrange 

is defined as the out-of-plane distance traveled 

by the vehicle from atmospheric interface to landing. 

Miss distance is defined as the distance between the 

targeted landing site and the actual landing site. For 

the purposes of this study, an acceptable footprint was 

defined as the region within which the CM achieved a 

miss distance of 3.5 km or less. 

Assumptions 

Several assumptions were made for the analysis 

performed in this study. The atmosphere was assumed 

to be the 1962 U.S. Standard Atmosphere to facilitate 

comparison with original Apollo program data. All 

entries were assumed to be posigrade equatorial. The 

entry state used is given in Table 1. The entry vehicle 

used was a scaled Apollo CM, as outlined in the 

ESAS, [2] with a maximum diameter of 5 m. Hypersonic 

blunt body aerodynamics were used, and the vehicle 

was flown at trim angle of attack, generating a lift-todrag 

ratio (L/D) of 0.4. Entry vehicle properties are 

summarized in Table 2. 

Table 1. Vehicle Entry State. 

Parameter Value 

Inertial Velocity 11032 m/s 

Altitude 122 km 

Longitude 0 deg 

Latitude 0 deg 

Azimuth 90 deg 

Table 2. Vehicle Properties. 

Parameter Value 

Mass 8075 kg 

Reference Area 23.758 m 2 

L/D 0.4 

Parameters Varied 

Crossrange commands were varied between 0 km and 

1000 km; downrange commands were varied between 

1500 km and 13000 km. This set of commands fully 

captured the capability footprint of the entry vehicle. 

Three flight path angles were selected to examine vehicle 

footprints over a range of atmospheric interface 

conditions, as shown in Table 3. Two of the FPAs were 

selected based on a CEV emergency ballistic entry (EBE) 

study conducted at the Charles Stark Draper Laboratory 

in September 2005. This set of parameters was 

used with both the baseline skip trajectory guidance 

and the high and low lofting versions of the enhanced 

skip trajectory guidance. 

26 Improving Lunar Return Entry Footprints Using Enhanced Skip Trajectory Guidance 

Table 3. Flight Path Angle Selections. 

FPA Selection Criteria 

-5.635 deg Center of aerodynamic corridor 

-5.900 deg Approximate shallow boundary for EBE 

-6.100 deg Approximate steep boundary for EBE 

results: Baseline algorithm 

Baseline Algorithm Description 

The primary function of the entry guidance algorithm 

is to manage energy as the spacecraft descends to the 

parachute deploy interface. The bank-to-steer algorithm 

controls lift in the coupled vertical and lateral channels, 

with guidance cycles occurring at a frequency of 0.5 

Hz. 

Guidance’s chief goal is to manage lift in the vertical channel 

so that the vehicle enters into the wind-corrected parachute 

deploy box at the appropriate downrange position. 

For a given FPA, full lift-up provides maximum range while 

full lift-down provides the steepest descent. Lift-down may 

be constrained by the maximum allowed g-loads that can 

be experienced by the crew and vehicle. Any bank orientation 

other than full lift-up or full lift-down will result 

in a component of lift in the lateral channel. Crossrange 

position is controlled in the lateral channel by reversing 

the lift command into the mirror quadrant (e.g., +30 deg 

from vertical to -30 deg) once the lateral range errors to the 

target cross a threshold. The vehicle continues this bank 

command reversal strategy as it descends to the target. As 

the energy and velocity decrease, the lateral threshold is 

reduced so that the vehicle maintains control authority to 

minimize the lateral errors prior to chute deploy. 

The baseline Apollo algorithm consists of seven phases 

designed to control the downrange position of the vehicle, 

as shown in Figure 2. 

Altitude (km) 

140 

120 

100 

80 

60 

40 

20 

0 

Initial Roll & Constant Drag 

Huntest & Constant Drag 

Down Control 

Up 

Control 

Targets 

Exit 

Conditions 

Kepler 2 nd Entry 

0 2000 4000 6000 8000 

Downrange Travelled (km) 

Figure 2. Baseline algorithm entry guidance phases.

(1) Preentry Attitude Hold: maintains current attitude 

until a sensible atmosphere has been detected. 

(2) Initial Roll: seeks to guide the vehicle toward the 

center of the entry corridor, nominally commanding 

the lift vector upward, otherwise commanding 

the lift vector downward to steepen a shallow 

entry. 

(3) Huntest and Constant Drag: begins once atmospheric 

capture is ensured, triggered by an altitude 

rate threshold. This phase determines whether the 

vehicle will need to perform an upward “skip” in 

order to extend the vehicle’s range, decides which 

of the possible phases to use, and calculates the 

conditions that will trigger those phases. The 

algorithm transitions to the Downcontrol phase 

once a suitable skip trajectory is calculated; otherwise, 

the algorithm transitions directly to the Final 

(“Second Entry”) phase if no skip is needed. 

(4) Downcontrol: guides the vehicle to pullout using a 

constant drag policy. 

(5) Upcontrol: guides the vehicle along a reference 

trajectory, previously generated by the Huntest 

phase. This trajectory is not updated during the 

Upcontrol phase. The algorithm transitions into the 

Kepler phase if the skip trajectory is large enough 

to exit the atmosphere; otherwise, the algorithm 

transitions directly into the Final (“Second Entry”) 

phase. 

(6) Kepler (“Ballistic”): maintains current attitude 

along the velocity vector from atmospheric exit to 

atmospheric second entry. Exit and second entry 

transitions are defined to occur at an aerodynamic 

acceleration of 0.2 g. 

(7) Final (“Second Entry”): guides the vehicle along 

a stored nominal reference trajectory, calculated 

preflight. Once the velocity drops below 

a threshold value, the algorithm stops updating 

bank commands and the guidance algorithm is 

disabled. 

The guidance phases and phase-transition logic are 

discussed fully in Reference [7]. 

Results Summary 

The results presented below are given in footprint plots. 

These plots show the miss distance associated with a 

particular downrange and crossrange command. Dark 

blue areas indicate accurate landings, while red areas 

indicate large miss distances. Light blue and dark blue 

areas provide acceptable accuracy, corresponding to 

miss distances of 3.5 km or less. It should be noted that 

red areas denote miss distance of 10 km or greater, with 

some miss distances in excess of 1000 km. 

Baseline Algorithm Results 

The entry guidance algorithm used for the Apollo 

program was selected as the baseline algorithm for 

the CM entry guidance. Figures 3-5 show the landed 

accuracy over a range of downrange and crossrange 

commands for several FPAs (see Table 3). Figure 4 

shows the footprint outlines at several FPAs. 

Figure 3 shows the footprint for the baseline algorithm 

at an FPA of -5.635 deg. Maximum crossrange is 

approximately ±700 km. Minimum downrange is 2250 

km; maximum downrange is 7000 km. Within these 

ranges, the algorithm performs well. Figure 4 shows the 

footprint for the baseline algorithm at an FPA of -5.900 

deg. Performance remains similar at this FPA. The minimum 

downrange decreases to 2000 km, while the maximum 

downrange remains 7000 km, with the exception 

of crossranges less than ±50 km. Some improvement is 

made in long-range performance, but accurate regions 

are patchy. Figure 5 shows the footprint for the baseline 

algorithm at an FPA of -6.100 deg. Significant performance 

improvements are visible at this FPA. Maximum 

downrange increases to 7500 km; minimum downrange 

is 2000 km. Maximum crossrange increases to ±750 km 

at large downranges. Long-range performance becomes 

accurate in two regions at crossranges greater than 400 

km. 

Crossrange Command (km) 

1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 

Downrange Command (km) 

Figure 3. Baseline miss distance (km) with FPA = -5.635 deg. 

Improving Lunar Return Entry Footprints Using Enhanced Skip Trajectory Guidance 27 

10+ 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0





Overall, the baseline algorithm provides good performance 

over downrange commands between 2000 km and 7000 km 

with crossranges up to 700 km, as shown in Figure 6. However, 

improvement is required for long-range performance. 


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 


2000 4000 6000 8000 10000 12000 


FPA = -5.653 deg 

FPA = -5.900 deg 

FPA = -6.100 deg 

Figure 6. Baseline range capability over several FPAs, miss 

distance

Next, the Final phase reference trajectory was redefined 

and extended to recenter it with respect to the CEV’s 

range capability, since the CEV has different vehicle 

characteristics from the Apollo CM. Finally, the Final 

phase range estimation method used by the Huntest and 

PredGuid phases was updated to enable the new Final 

phase reference trajectory to support a wider spread 

of target ranges. More detail about the enhancements 

made to the algorithm is available in Reference [9]. 

The affects of modulating the start time of the PredGuid 

phase was also investigated. A comparison was made 

between starting the PredGuid phase at the beginning 

of the Upcontrol Phase (as described above) and starting 

the PredGuid phase at the beginning of the Downcontrol 

phase. The difference in these two approaches 

resulted in different trajectory shaping. Starting the 

PredGuid phase at the nominal time by replacing the 

Upcontrol and Kepler phases resulted in a lower-altitude, 

shallower skip trajectory. Starting the PredGuid 

phase earlier by also replacing the Downcontrol phase 

resulted in a higher-altitude, steeper lofting. 

Enhanced Algorithm Results 

The results presented below detail the entry footprint of 

the CM using the enhanced numerical predictor-corrector 

guidance algorithm with both high and low lofting. 

Figures 8-13 show the landed accuracy, in terms 

of miss distance, of the CM at various downrange and 

crossrange commands for a given FPA. Figures 11 and 

12 show the footprint outlines for high and low lofts 

for several FPAs. 

Figure 8 shows the footprint for a low loft at an FPA of 

-5.635 deg. The CM achieves a maximum crossrange 

of approximately ±750 km. The minimum downrange 

is 2250 km and significant accuracy is lost when 

downranges greater than 10000 km are targeted. The 

footprint for a low loft at an FPA of -5.900 deg is shown 

in Figure 9. The CM achieves a maximum crossrange of 

±850 km, an increase of 100 km over the -5.635 deg case. 

The minimum downrange decreases to 2000 km from 

2500 km in the -5.635 deg case. Significant accuracy 

is still lost when downranges greater than 10000 km 

are targeted. The footprint for a low loft at an FPA of 

-6.100 deg is nearly identical to that of the -5.900 deg 

case (Figure 10). Of note is the much larger red region 

starting at 11000 km, indicating a deterioration of longrange 

performance with steepening FPA. 


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 


Figure 8. Low loft miss distance (km) with FPA = -5.635 deg. 




1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 



Improving Lunar Return Entry Footprints Using Enhanced Skip Trajectory Guidance 29 

10+ 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

10+ 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

10+ 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0

Figure 11 shows the footprint for a high loft at an FPA 

of -5.635 deg. The CM achieves a maximum crossrange 

of approximately ±900 km, a 150-km increase over the 

low loft case. The minimum downrange is 2250 km and 

the maximum downrange is 11250 km. No accuracy is 

lost between 10000 km and 11250 km as in the low loft 

case. The footprint for a high loft at an FPA of -5.900 deg 

is slightly better (Figure 12). The CM achieves a maximum 

crossrange of ±950 km. The minimum downrange 

is 2000 km and the maximum downrange is 11000 km, 

slightly less than the -5.635 deg case. Of particular note 

are two regions of inaccuracy near 3000 km downrange. 

Figure 13 shows the footprint for a high loft at an FPA 

of -6.100 deg. The CM achieves a maximum crossrange 

of ±900 km. Downrange performance is similar to the 

-5.900 deg case. The two inaccurate regions near 3000 

km downrange have disappeared at this FPA. 


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 


Figure 11. High loft miss distance (km) with FPA = -5.635 

deg. 


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 



deg. 

30 Improving Lunar Return Entry Footprints Using Enhanced Skip Trajectory Guidance 

10+ 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

10+ 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

2000 4000 6000 8000 10000 12000 



deg. 

Figures 14 and 15 show the footprints for low and 

high loft trajectories, respectively, at three FPAs. The 

footprint outlines correspond to miss distances of 3.5 

km or less. As shown before, -5.900 deg and -6.100 

deg provide similar performance, while -5.635 deg is 

slightly less capable. All trajectories begin to lose accuracy 

beyond 10000 km. As in the low loft cases, the 

performance of the high loft -5.900 deg and -6.100 

deg cases is similar, with the exception of the two inaccurate 

regions in the -5.900 deg case near 3000 km 

downrange. The -5.635 deg case is slightly less capable 

in minimum downrange and maximum crossrange, but 

slightly more capable in maximum downrange, providing 

capability to 11250 km. 


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

FPA = -5.635 deg 

FPA = -5.900 deg 

FPA = -6.100 deg 

2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 


Figure 14. Low loft footprints for several FPAs, miss 

distance


1000 

800 

600 

400 

200 

0 

-200 

-400 

-600 

-800 

-1000 

FPA = -5.635 deg 

FPA = -5.900 deg 

FPA = -6.100 deg 

2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 


Figure 15. High loft footprints for several FPAs, miss 

distance

eferences 

[1] The White House Website Presidential News and Speeches, 

“President Bush Announces New Vision for Space Exploration 

Program,” URL: http://www.whitehouse.gov/news/releases/2004/01/20040114-3.html, 

October 26, 2005. 

[2] Exploration Systems Architecture Study Final Report, NASA 

TM-2005-214062, November 2005. 

[3] NASA Solicitation: Conceptual Design of an Air Bag Landing 

Attenuation System for the Crew Exploration Vehicle, Langley 

Research Center Press Release, December 14, 2005. 

[4] Graves, C.A. and J.C. Harpold, Reentry Targeting Philosophy 

and Flight Results from Apollo 10 and 11, MSC 70-FM-48, 

March 1970. 

[5] Tigges, M. et al., Earth Land-Landing Analysis for the First 

Lunar Outpost Mission: Apollo Configuration, NASA JSC- 

25895, June 1992. 

[6] Putnam, Z.R. et al. “Entry System Options for Human Return 

from the Moon and Mars,” AIAA 2005-5915, AIAA Atmospheric 

Flight Mechanics Conference, San Francisco, CA, 

August 2005. 

[7] Morth, R., Reentry Guidance for Apollo, MIT/IL R-532 Vol. I, 

1966. 

[8] DiCarlo, J.L., Aerocapture Guidance Methods for High Energy 

Trajectories, SM Thesis, Department of Aeronautics and 

Astronautics, MIT, June 2003. 

[9] Bairstow, S.H., Reentry Guidance with Extended Range Capability 

for Low L/D Spacecraft, SM Thesis, Department of 

Aeronautics and Astronautics, MIT, February 2006. 

32 Improving Lunar Return Entry Footprints Using Enhanced Skip Trajectory Guidance

(l-r) Zachary R. Putnam, 

Gregg H. Barton and 

Robert D. Braun 

bios 

Zachary R. Putnam performed 

his graduate 

research work in the area 

of entry system design 

and performance. He 

currently supports the 

development of skip entry guidance for NASA’s Crew Exploration Vehicle at Draper’s Johnson Space Center field site. He 

holds an MS in Aerospace Engineering from Georgia Tech. 

Robert D. Braun is an Associate Professor in the Guggenheim School of Aerospace Engineering at the Georgia Institute of 

Technology. As Director of Georgia Tech’s Space Systems Design Laboratory, he leads a research and education program 

focused on the design of advanced flight systems and technologies for planetary exploration. In addition, Dr. Braun 

provides consulting services in the areas of space systems engineering and analysis, planetary entry, and Mars atmospheric 

flight. He has provided independent analysis and review services for the Mars Global Surveyor, Mars Odyssey, Mars 

Exploration Rover, Genesis, Phoenix Mars Scout, and Mars Science Laboratory flight projects. Dr. Braun received a BS in 

Aerospace Engineering from Penn State (1987), an MS in Astronautics from the George Washington University (1989), 

and a PhD in Aeronautics and Astronautics from Stanford University (1996). 

Sarah H. Bairstow performed her Master’s thesis research on the topic of reentry guidance algorithms for low L/D spacecraft 

as a Draper Fellow under the advisement of Gregg Barton, after which she began full-time employment at Draper to 

expand on that research. She has been employed since June 2006 as a Space Mission Systems Concept Analyst at the Jet 

Propulsion Laboratory in Pasadena, CA. She received an MS in Aeronautics and Astronautics from MIT (2006). 

Gregg H. Barton has been with the Laboratory since 1985 and is currently the Group Leader for the Mission Design and 

Analysis for Earth, Moon, and Mars GN&C systems, and the Draper Project Lead for Skip Guidance Technologies for 

Earth return vehicles. Responsibility over the years includes all levels of project development from requirements and 

interfaces, concept design and analysis, algorithm and software development, and test and verification for flight certification. 

Management duties have included all levels from task lead, project lead, technical director, proposal manager to 

program manager. In addition to these duties, he has served as technical supervisor and mentor for new staff and MIT 

graduates. 

Improving Lunar Return Entry Footprints Using Enhanced Skip Trajectory Guidance 33

34 

A Deep Integration Estimator 

for Urban Ground Navigation 

Dale Landis, Tom Thorvaldsen, Barry Fink, Peter Sherman, Steven Holmes 

Copyright © 2006, IEEE. Presented at IEEE PLANS, San Diego, CA, April 25-27, 2006 

abstract 

The objective of the Personal Navigator System (PNS) is to 

construct a wearable navigation system that provides accurate 

position over extended missions in a deprived Global 

Positioning System (GPS) environment. The prototype 

multisensor navigator included a set of micromechanical 

inertial sensors, a three-axis miniature radar, a selective 

availability antispoofing module (SAASM) GPS receiver, 

and a barometric altimeter. Real-time embedded software 

sampled sensor data, controlled GPS receiver tracking 

loops, and hosted a multisensor optimal estimator whose 

output position was transmitted via wireless link to a highresolution 

personal data accessory (PDA) tracking display. 

The fully packaged system was field tested in Cambridge, 

Massachusetts under realistic, GPS-stressed conditions. 

This paper focuses on the deep integration (DI) algorithm 

design used for the optimal estimation of both position 

and receiver tracking control. The algorithm was tailored 

here for intermittent GPS visibility on the ground and in 

outdoor-indoor-outdoor maneuvers. DI has been used 

previously for missile guidance, navigation, and control 

with clear sky view. 

The PNS required an optimal estimator that combined 

the nonlinear GPS/inertial DI algorithm with measurements 

from other sensors. The mission duration here 

was much longer, and the satellite environment over the 

ground track was highly variable compared with earlier 

DI applications. This required the development of strategies 

for dropping satellites from track after long blockage 

times and for taking control of newly visible satellites 

under DI tracking. Here, the advantage of DI tracking 

is the ability to extract GPS pseudorange information 

almost instantly if a satellite reappears momentarily from 

a blockage. 

This paper reviews the DI approach with stress on the 

receiver correlator power measurements, nonlinear filter 

equations, and the calculation of numerically-controlled 

oscillator (NCO) commands. Specific problems encountered, 

such as clock error recalculation and numerical 

issues, will be mentioned. Urban canyon performance data 

demonstrating accurate navigation under sparse GPS availability 

are also described.

Introduction 

The PNS is a small package containing a Draper Laboratory 

micromechanical inertial measurement unit (IMU), a Rockwell 

Collins GPS receiver, a triad of Doppler radar velocity 

sensors, a barometric altimeter, a PDA that allows human 

user interface, and a processor that contains Draper-developed, 

real-time navigation software. This package is wearable 

in a front-mounted configuration by a foot soldier, and 

its objective is to provide long-term accurate coordinates in 

both outdoor and indoor environments, including significant 

periods of GPS signal deprivation. 

The software comprises strapped-down navigation algorithms 

combined with Draper’s deep integration (DI) nonlinear filter 

for processing GPS correlator outputs, based on previous 

Draper munitions shell applications. Doppler updates, navigation 

initialization, and satellite line-of-sight (LOS) error estimation 

were among the many features added for the application. 

Demonstration in a full hardware mode was done in Spring 

2005. An example is shown in Figure1. 

Up (ft) 

Position NEU 

Recorded 3-D Track 

In-Building 

GPS-Denied 

20 

0 

-20 

Finish 

-40 

-60 

-80 

200 

450 

400 

150100 Rooftop Start 

350 

300 

50 Sky in Full View 250 

0 

200 

150 

East (ft) -50 100 

50 

North (ft) 

-100 

0 

Figure 1. Real-time PNS test results in Technology Square, 

Cambridge. 

The test illustrated involved an outdoor phase followed 

by an indoor GPS-deprived period. Figure 1 shows that 

position accuracy was maintained, even during the indoor 

phase. An overlay of the recorded track onto geolocated 

floor plans showed very good registration with hallways. 

In the vertical direction, stairwell landings are clearly seen. 

The PNS effectively locates the user to the correct floor. 

The tests also showed that on return to the outdoor environment, 

GPS resumed almost immediately. Results of this 

test program were reported at JNC’05. [1] 

The algorithm that accomplished this performance is 

surveyed in subsequent sections, with emphasis on the 

components that required fresh techniques. 

Navigation algorithm and related Calculations 

The inputs to the navigation algorithm are 100-Hz sampled 

specific force (accelerometers) and rate (gyroscopes) in a 

PNS orthogonal body-fixed frame that is designated by b 

in this paper. The core of the PNS navigation algorithm is a 

standard strapped-down integration algorithm comprising 

IMU compensation, quaternion third-order integration, 

gravity compensation of accelerometer outputs, and velocity 

and position integration in earth-fixed, earth-centered 

(ecef or e) coordinates. For future reference, the navigation 

major outputs are: 

= position e frame 

= velocity e frame 

q = quaternion b to e 

= direction cosine matrix 

Navigation initialization, omitting many details, is as 

follows. The receiver begins with conventional acquisition 

and tracking, downloads ephemeris, and sends a position 

and velocity to navigation. A crude azimuth estimate 

is made by assuming an initial north and level orientation 

(accuracy of 10 deg in azimuth is sufficient). Once 

the receiver enters deep integration mode (less than a 

minute), the wearer moves horizontally, and the filter is 

able to refine the attitude estimates sufficiently for continued 

operation using the difference between IMU- and GPSdetermined 

accelerations. Current work at Draper includes 

more advanced forms of attitude initialization that impose 

less artificial restraints on the PNS wearer. 

In addition to navigation proper, there are calculations that 

keep track of optimal estimates of other quantities, primarily 

the following: 

dtR = user (receiver) clock bias 

d = user clock frequency error 

db k = LOS delay error satellite k 

An error filter based on perturbation of the navigation algorithm 

is used to process all the measurements. The filter 

states are listed for future reference in Table 1. 

Table 1. PNS Filter States. 

Error States Units 

Position dr 3 chips 

Velocity dv 3 chips/s 

Attitude y 3 rad 

Gyro Bias Shift 3 rad/s 

Gyro Bias Markov 3 rad/s 

Accel. Bias Shift 3 chips/s 2 

Accel. Bias Markov 3 chips/s 2 

User Clock Bias 1 chips 

User Clock Frequency 1 chips/s 

Doppler Misalignment (6) 6 rad 

Satellite Delay 12 chips 

Altimeter Bias 1 chips 

A Deep Integration Estimator for Urban Ground Navigation 35

The chip units are defined for P code (which is used in 

PNS) by 96.146 ft/chip or 9.775 x 10 -8 s/chip. 

The filter performs the GPS DI updates plus Kalman 

updates for the other sensors. A set of corrections for 

the navigation system and clock model are computed 

and then fed back to the navigation algorithm for a 

reset of the full system state. 

The algorithm-embedded software is coded in three rate 

groups: high (100 Hz), medium (50 Hz), and low (10 

Hz). High rate performs IMU compensation, attitude 

integration, and incremental transition matrix calculations. 

Medium rate performs navigation position and 

velocity integration, bookkeeping of the receiver clock 

error estimate and satellite atmospheric delay estimates, 

and all GPS receiver interfacing (described below). 

Both high and medium rate perform resets based on 

corrections supplied by the nonlinear filter. Low rate 

performs all filter updates and sends corrections to high 

and medium rate. 

Deep Integration GPs 

Background of Draper’s Deep Integration 

DI was developed to extend GPS tracking to poor 

GPS signal-to-noise conditions, especially intentional 

jamming environments. Deep integration requires 

a custom receiver configured so that the navigation 

software can issue the numerically controlled oscillator 

(NCO) commands (overriding the internal tracking 

loops) and also receive integrated correlator outputs. 

For previous results with DI, see Ref. [2]. 

Prior to PNS, Draper DI was used successfully in artillery 

shells with high dynamics and short duration, where 

the instrumentation was limited to inertial sensors and 

the receiver. 

For the personal navigator, Draper extended the use 

of DI in significant ways. First, mission duration in 

the tests was stretched from minutes to one half hour. 

There is no inherent mission duration limitation here. 

Second, the capability of the nonlinear algorithm was 

extended to perform both the nonlinear GPS updates and 

conventional Kalman updates (from the Doppler radar 

and altimeter). In contrast to the fixed set of satellites in 

view for a short time-of-flight missile, the ground navigation 

system described here needed to adapt to satellite 

configuration changes. Finally, of course, this was 

all done with hardware compressed to a point practical 

for use by a foot soldier. 

A key advantage of DI for the ground navigation application 

is the ability to recover satellite track after signal 

36 A Deep Integration Estimator for Urban Ground Navigation 

is temporarily lost, perhaps due to masking from a 

landscape fixture. A second advantage is that deep integration, 

by design, is able to track a satellite when its 

power is weaker, due to factors such as forest canopy or 

indoor attenuation. 

Summary and Technical Overview 

In conventional operation, the GPS receiver is based 

on internal tracking loops, in which tracking loops are 

maintained for GPS code and carrier signals, based on 

correlator outputs and NCO commands, both of which 

are invisible to the end user. The user is supplied with 

pseudo and delta range information tapped from these 

loops, or final position and velocity. Conventional GPS 

is covered in numerous sources, among which Ref. [3] 

may be cited. 

In deep integration, the correlator outputs are issued to 

the navigation processor, along with a code phase (or 

equivalently, pseudorange) for the replica signal. The 

navigation software sends rate commands to the receiver 

NCOs, which the receiver uses to generate the replica 

signal. This operation replaces the internal loops. 

In practice, there is an alternation between modes in 

PNS. Sometimes (initially and during extended signal 

loss), the receiver maintains control of tracking loops. 

Whenever possible, internal loops are replaced by the 

DI process. These modes are referred to as “receiver 

control” (internal loops) and “host control” (deep 

integration). 

Description of PNs Deep Integration 

A compressed technical summary of deep integration 

can be given by reference to the main interfaces in PNS, 

shown in Figure 2. First, the code and carrier NCO 

commands issued to the receiver are discussed in detail. 

Then the receiver outputs sent to navigation and their 

transformation into filter observations are discussed. 

Finally, the filter corrections applied to the navigator 

are discussed. 

GPS 

Receiver 

I, Q, r* 

50 Hz 

. . 

tcode , tcarr Navigation 

Medium 

Rate 

10 Hz 

Corrections 

Figure 2. Deep integration interfaces in PNS. 

dz 

PNS Processor 

Navigation 

Low 

Rate

The 50-Hz rate command that the navigator gives to the 

code NCO is a code phase rate, which may be given in 

speed of light units as: 

where tcorr is a “correction” to bring the code phase to 

the navigation predicted position, and the reflects 

navigation predicted rate. Dt is the time interval of the 

NCO command application (20 ms). 

The correction term, also referred to as the NCO “poke,” 

is represented by: 

where 

= user time bias estimate 

= range-to-satellite estimate 

= atmospheric delay estimate 

= satellite clock bias estimate 

r* = replica code pseudorange 

The range term is calculated from navigation position, 

and the clock error is derived from the navigation filter. 

r* is the receiver-supplied pseudorange. 

It is instructive to see a derivation of this command. 

Navigation information may be used to calculate the 

time (referenced to the satellite clock) of transmission 

of a light pulse currently received, which is the calculated 

satellite signal code phase. This is: 

where tR is receiver user time. The receiver sends a 

measured replica code pseudorange, from which the 

replica code phase may be calculated as: 

t* = tR – r* (4) 

The goal is to drive the replica code to a phase where, 

according to navigation and clock estimates, it would 

match the incoming code from the satellite. The alteration 

of code phase that accomplishes this is: 

tcorr = tcalc – t (5) 

If Eqs. (3) and (4) are substituted into Eq. (5), the result 

is precisely Eq. (2). 

(1) 

(2) 

(3) 

The second term (also called the “push”) in the command 

is: 

where 

= user time frequency error estimate 

A Deep Integration Estimator for Urban Ground Navigation 37 

(6) 

= range rate estimate (from navigation velocity) 

= satellite clock frequency error estimate 

In the current DI configuration, the carrier NCO is also 

commanded by the push term derived above. This is 

sufficient to maintain the accuracy of the P code tracking, 

which is the primary information source for the 

PNS. 

Note that these commands have the following effect: 

replica code is lined up with navigation prediction. As 

a consequence, the correlator information will make the 

navigation errors (including PNS clock error estimates) 

directly observable. This forced observability of navigation 

error in I and Q (in phase and quadrature) output 

is fundamental to deep integration. 

Using the NCO commands to generate the replica code, 

the receiver produces I and Q integrated correlator 

outputs in the standard way. (See for example Ref. [3].) 

As shown in Figure 2, the receiver sends these I and Q 

data, integrated over 20-ms intervals, to the navigation 

medium rate function. At each time, these are indexed 

over the satellite set (N) and over the number of correlators, 

T = 2K + 1 (5 for PNS). 

The navigation medium rate task compresses these by 

summing their squares over five time samples. Using 

i for the time index (i = 1,...,5), k for the correlation 

index (k = 1,...,T), and suppressing the satellite 

(receiver channel) index, the measurement is: 

For each 100-ms interval, this gives a T-element vector 

measurement (in contrast to conventional loops that 

form a scalar measurement, gaining local linearity at the 

cost of information). The vector measurement for one 

satellite for one 10-Hz filter pass is readily derived from 

standard equations for I and Q data giving: 

(7)

where 

dt = 20 ms 

S = signal power 

R = pseudorandom code correlation function 

e = LOS delay error in chips 

D = correlator spacing = 0.5 chip 

b = bias 

n = noise 

The bias and noise both derive from squaring the raw I 

and Q noise and equations for their distributions may 

be derived. The ideal correlation function is: 

Finally, the LOS error is modeled as: 

38 A Deep Integration Estimator for Urban Ground Navigation 

(8) 

(9) 

(10) 

where u is a unit vector from the IMU to the satellite, 

dba is the residual atmospheric delay error, and dtR is 

user clock residual error. 

The DI filter first uses the dz measurements to estimate 

the signal-to-noise ratio (SNR), allowing for smooth 

adaptation to jamming or low signal strength. Then, the 

DI filter performs an update of the filter error state. The 

details of this update algorithm are omitted here. Since 

the measurement model is highly nonlinear due to the 

form of R and its square, common Kalman methods 

must be replaced by algorithms from nonlinear estimation 

theory. Further discussion is in Ref. [4]. 

The remaining arrow in Figure 2 shows the low to 

medium rate transfer of corrections. After all estimates 

are processed for one 10-Hz filter pass (all satellites, 

plus radar and altimeter measurements), the error state 

is used to calculate these corrections. At the end of the 

next 10-Hz interval, the navigation system incorporates 

these corrections in a reset. The following items 

are reset based on filter error states: position, velocity, 

quaternion, gyroscope, and accelerometer compensators, 

user clock error estimates, and LOS delay errors 

for satellites being tracked. 

The two-rate scheme of Figure 2 is critical to the operation 

of DI GPS. The data from the filter are not sent 

directly to the receiver. Rather, the corrections go to 

medium rate, and then indirectly affect NCO commands 

via the 10-Hz resets. The 50-Hz receiver control allows 

for tracking high-frequency dynamics in the correlators, 

while the lower rate filter execution allows for a 

more advanced estimation algorithm with more accurate 

estimates. 

Clock errors: Initialization and reacquisition 

Timing and clock errors are critical to deep 

integration. 

The previous section indicated how the navigation filter 

kept up accurate clock error estimates while tracking 

satellites in deep integration. Two closely related problems 

are clock initialization and clock recapture after 

satellite signal loss. 

Time is determined in navigation on the basis of highspeed 

interrupts from the Rockwell Collins receiver, 

referred to as t10 (10 ms apart) and t1000 (1 second 

apart). These are driven directly by the receiver 

oscillator. 

Navigation time, or user time, is based directly on 

a count of t10 interrupts. The user clock bias and 

frequency errors are defined in speed-of-light units as: 

dtR = user time – GPS time 

= user time frequency – true frequency 

For practical purposes, GPS time is considered perfect. 

True frequency is, in speed-of-light units, 1 + Doppler. 

As seen above, estimates of these enter into navigationissued 

NCO commands. From this follows the deep 

integration requirement: clock estimates must always 

be within about a chip (approximately 100 ft) of accuracy 

to retain code lock in deep integration. 

Initialization: At initial operation, the receiver is 

in control of its NCOs, and the navigation software 

receives t1000 interrupts and messages with the matching 

GPS times. The navigation wrapper software does 

careful bookkeeping of these data over at least three 

low-rate passes (t1000 interrupts). From this, a linear 

relationship between user and GPS time can be determined 

algebraically. The data are then passed to the 

navigation algorithm, which in turn (after navigation 

initialization), issues a command to the receiver to 

accept host control. 

Reacquisition: After a long period of time without visible 

GPS satellites, it was found that the receiver clock can 

drift nonlinearly to a point well outside the 100-ft accuracy 

requirement. An immediate return to DI updates 

would result in the loss of lock and poor performance 

of the PNS navigator.

An elementary solution based on a quick coarse clock 

recalibration was developed. The solution assumes that 

the time of GPS signal loss is sufficiently short so that 

the navigation position error has maintained relative 

accuracy (about 150 ft). This condition can be readily 

checked from filter variances. On return of signal power 

from one satellite, the navigation software calculates a 

candidate tcorr (see Eq.(2)), but instead of sending it 

to the receiver as an NCO command, it replaces the 

current clock error estimate with this value. Likewise, a 

difference in two tcorr calculations is assigned as clock 

frequency error. At the same time, filter variances are 

opened to indicate the coarseness of these estimates. 

At this point, the navigator again takes control of the 

NCOs, and subsequent filter passes allow for further 

refinement of clock and position errors. 

For the PNS tests conducted in 2005, the position errors 

were well under 150 ft, thus supporting the validity 

of the algorithm described above. Draper is currently 

investigating methods to extend the clock correction to 

relax the restriction on small position error. 

Doppler radar 

The Doppler radar sensors provide a three-dimensional 

velocity vector using short-range, low-power transceivers. 

The Doppler measurement is crucial to PNS 

in situations where GPS signals are unavailable, since 

it is the primary means (along with the altimeter) of 

damping position, velocity, and attitude drift inherent 

in the strapped-down navigation system. Tests 

have demonstrated that the Doppler allows for excellent 

performance indoors (with no GPS signals) for 

extended periods; furthermore, by keeping position 

errors bounded, it enables quick return to the GPS deep 

integration mode when satellite signals return. 

There are three Doppler sensors nominally in an 

orthogonal frame (designated dopp), with the sensing 

axes aligned so that in normal walking motion, each 

will reflect a signal off the floor or ground. Each sensor 

outputs 512 measured amplitudes from the reflected 

signal over 0.1 s, providing 2 cm/s Doppler resolution. 

The data are sent to the 10-Hz navigation function, 

which shifts the raw signal to baseband, performs a 

fast Fourier transform, then applies the Doppler law to 

derive LOS velocity. This velocity is shifted to the IMU 

center, giving a final processed Doppler measurement 

from the triad of: 

(11) 

This represents earth-relative velocity of the IMU center 

in the Doppler axis frame. The velocity is not instantaneous 

but an average over the 0.1-s interval of validity. 

The measurement is linearized for a Kalman update 

for the navigation error states. The filter observation is 

calculated as: 

(12) 

The bar over the navigation velocity indicates an average 

over the interval of validity. 

Finally, an error model for this measurement was 

derived by taking differentials. Showing only the most 

important terms, the resulting model is: 

(13) 

The error states in Eq. (13) are defined in Table 1. 

The Doppler error term consists of Doppler input axis 

misalignments (modeled by individual axis, not shown 

here) and discrete measurement noise. 

The fact that Equation 13 employs Doppler coordinates, 

rather than ecef, has major advantages. In these axes the 

three scalar measurements can be modeled with independent 

noise, and the three scalar updates can be done 

sequentially. This allows skipping or performing updates 

on a sensor-by-sensor basis, in response to sensor output 

validity indicators. The power level output by the Doppler 

sensors is used for this purpose. If one or two Dopplers 

measure very low power, this is taken to indicate invalid 

axes; for example, an axis may be pointing to a very 

distant reflector or to infinity. If all three axes read low 

power and other sanity checks are met, this indicates a 

stand-still event, and a zero velocity update is executed 

instead. 

Also note that the Doppler observation is a combination 

of velocity and attitude error, a consequence of the fact 

that it measures in a body-fixed frame, in contrast to 

GPS, which measures velocity in the earth-fixed frame. 

This can often create interesting results. For example, if 

GPS signals are strong and velocity is accurate, attitude 

can be improved by the Doppler. On the other hand, 

in a GPS-deprived scenario, attitude error can limit the 

improvement of navigation position accuracy. 

summary 

Results have shown that Draper’s configuration of deep 

integration GPS combined with other sensors is a practical 

design for a personal navigator. This paper has 

illustrated the main features of the algorithm design. 


acknowledgment 

This material is based on work supported by the 

U.S. Army/Natick Soldier Center under Contract No. 

DAAD16-02-C-0040 C 2005, The Charles Stark Draper 

Laboratory, Inc. 

references 

[1] Sherman, P., A. Kourepenis et al., “Personal Navigation for 

the Warfighter,” JNC’05. 

[2] Gustafson, D. and J. Dowdle, “Deeply Integrated Code Tracking: 

Comparative Performance Analysis,” 16 th International 

Technical Meeting of the Satellite Division of the Institute of 

Navigation, Portland OR, September 2003. 

[3] Kaplan, E.D., Understanding GPS: Principles and Applications, 

Artech House, 1996. 

[4] Gustafson, D., J. Dowdle, and K. Flueckiger, “A Deeply Integrated 

Adaptive GPS-Based Navigator with Extended-Range 

Code Tracking,” IEEE PLANS Conference, San Diego, March 

2000. 

40 A Deep Integration Estimator for Urban Ground Navigation

(l-r) Peter Sherman, 

Steven Holmes, 

Dale Landis and 

Tom Thorvaldsen 

bios 

Dale Landis is a Principal 

Member of Technical Staff 

at Draper Laboratory. His 

specialties include estimation 

theory, navigation algorithms, 

and applied mathematics. 

He has contributed software 

for munitions, satellites, and 

personal navigators. He received a Draper Distinguished Performance Award as a member of the team that first demonstrated 

the Draper deep integration algorithm on a GPS receiver; much of his recent work is aimed at the maturity and range of 

application of deep integration. Dr. Landis has a PhD in Mathematics from Lehigh University. 

Tom Thorvaldsen is a Distinguished Member of the Technical Staff and Group Leader for Navigation and Localization. He has 

been responsible for the design, architecture, and data analysis of numerous inertial navigation systems. He is on two patents 

and has received two Distinguished Performance Awards. He has been at Draper Laboratory since 1975 and holds a BS in 

Electrical Engineering from New Jersey Institute of Technology and an MA in Mathematics from the University of Michigan. 

Barry Fink is a Senior Member of Technical Staff at Draper Laboratory. He has been doing GPS work for 20 years. He has an 

MA in Mathematics from Boston University. 

Peter Sherman is a Principal Member Technical Staff, Special Operations and Tactical Systems, at Draper Laboratory. He was 

Technical Director of the successful Personal Navigation System project and continues as TD to the PNS follow-on. Prior to 

coming to Draper, he worked at Kearfott Guidance and Navigation developing a tactical-grade inertial multisensor – a singlechip 

gyro and accelerometer – using MEMS fabrication techniques. Also at Kearfott, he led software/system development and 

integration teams for ring-laser gyro (RLG)-based IMU and GPS/INS products. He was an Integrated Product Team (IPT) lead 

for the Joint Direct Attack Munition (JDAM) navigation subsystem on a Lockheed Martin-Kearfott team. Dr. Sherman is a 

member of IEEE, received a BS (Hon) from the University of Michigan and a PhD in Chemistry/Chemical Physics from the 

University of Oregon where he held an IBM Corp. Pre-doctoral Fellowship. 

Steven Holmes is a Senior Program Manager and currently leads Draper Laboratory’s efforts to become a CMMI Maturity 

Level III organization. In the recent past, he led Draper’s efforts to develop advanced ballistic and guided airdrop capabilities 

for the U.S. Army and Air Force, as well as efforts to develop a personal navigation system that provides accurate navigation 

information in a wide range of environments. He received a BS in Mathematics with a minor in Computer Science from 

Northeastern University (1987) and an MBA from Boston University (1994). 


42 

Error Sources in In-Plane Silicon 

Tuning-Fork MEMS Gyroscopes 

Marc S. Weinberg, Anthony Kourepenis 

Copyright © 2006 IEEE. Published in Journal of Microelectromechanical Systems, Vol. 15, No. 3, June 2006 

abstract 

This paper analyzes the error sources defining tacticalgrade 

performance in silicon, in-plane tuning-fork gyroscopes 

such as the Honeywell-Draper units being delivered 

for military applications. These analyses have not yet 

appeared in the literature. These units incorporate crystalline 

silicon anodically bonded to a glass substrate. After 

general descriptions of the tuning-fork gyroscope, ordering 

modal frequencies, fundamental dynamics, force and 

fluid coupling, which dictate the need for vacuum packaging, 

mechanical quadrature, and electrical coupling are 

analyzed. Alternative strategies for handling these engineering 

issues are discussed by introducing the Systron 

Donner/BEI quartz rate sensor, a successful commercial 

product, and the Analog Device (ADXRS), which is 

designed for automotive applications. 

Introduction 

The development of microelectromechanical systems 

(MEMS) inertial sensors offers revolutionary improvements 

in cost, size, and ruggedness relative to fiber-optic and 

spinning mass technologies. [1],[2] Driven by high-volume 

commercial market needs, applications continue to grow 

for modest performing components at prices below $10/ 

axis. The Army is funding a $100M initiative to realize 

producible, low-cost, tactical-grade MEMS inertial measurement 

units (IMUs) for gun-launched munitions and missile 

applications. The continued maturation of the technology 

will enable new applications and markets to be realized. 

This paper analyzes design considerations necessary to 

reach tactical-grade performance in a silicon MEMS tuningfork 

gyroscope (TFG) such as the Draper-based design that 

Honeywell is delivering in military systems. In the appendices, 

alternative strategies for handling these engineering 

issues are discussed by introducing the Systron Donner/

BEI quartz rate sensor, a successful commercial product, 

and the Analog Device (ADXRS), which is designed for 

automotive applications. 

While many universities, government organizations, and 

companies have done research or even advertised the availability 

of inertial sensors, only a handful produces inertial 

instruments on a commercial scale. University of California, 

Berkeley, [3]-[5] University of Sheffield, UK, [6] University 

of Newcastle, UK, [7] Seoul University, Korea, U. Neuchatel, 

Switzerland, [8] the Massachusetts Institute of Technology 

(MIT), Tohoku University, Japan, [9] Sandia, [10] Integrated 

Micro Instruments, [10] Cal Tech, Jet Propulsion Lab, [11] 

University of California, Los Angeles (UCLA), [11] National 

University of Singapore, [12] University of Michigan, [13],[14] 

Sagem, [15] and many others have published on MEMS 

gyros. Three hundred sixty eight MEMS fabrication facilities 

have been identified worldwide. [16] 

The MEMS angular rate sensor or gyroscope divides itself 

into tactical and automotive/commercial performance 

categories. Two companies are producing tactical-grade 

performance on the order of 1 to 10 deg/h. Several are 

producing automotive grade, which is loosely defined as 

several hundred to a few thousand deg/h. The scarcity of 

commercial sources despite the plethora of research efforts 

and advertisements underscores the difficulty in constructing 

MEMS angular rate sensors. 

Based on technology developed at Draper Laboratory, 

Honeywell is delivering HG1900, HG1920, and HG1930 

navigation systems. After a decade of excellent test data, 

production quantities are now being realized. In 2004, 

several hundred systems were delivered for military applications, 

such as artillery shell and mortar shell guidance. 

Discussed further in the next section, this gyro is crystalline 

silicon-on-glass and has two mechanically-coupled 

proof masses moving in antiparallel directions, and senses 

rate in the wafer substrate plane. 

Systron Donner/BEI has built hundreds of thousands of 

quartz TFGs over the past 15 years. [17],[18] For their higher 

performance units, quoted specification sheet performance 

is 36 deg/h/ noise, and uncompensated thermal sensitivities 

are 21 deg/h/°C and 300 ppm/°C. These sensors 

have been used in many higher performance automobiles 

for traction and stability control and in military systems. 

Automotive or commercial-grade angular rate sensors 

perform at several hundred to a few thousand deg/h. 

Analog Devices’ ADXRS150 specifies noise of 180 deg/h/ 

and uncompensated thermal sensitivities of 1440 deg/h/°C 

and 1700 ppm/°C (typical values are 180 deg/h/°C and 150 

ppm/°C). Analog employs polysilicon deposited over oxide 

sacrificial layers. Because of integrated on-chip electronics, 

these gyros are small and consume only 30 mW per axis. 

Silicon Sensing Systems, a collaboration of BAE Systems 

and Sumitomo, sells an automotive gyro consisting of a 

MEMS ring resonator driven by magnetic fields. Delphi 

pursued ring resonators for several years, but no information 

has been released in recent years. In their automotive 

products, Bosch has incorporated a rate sensor that 

can be purchased as a replacement part at BMW dealers. 

The sensor consists of two linear accelerometers supported 

in a vibrating frame. [19] Bosch employs a 10-µm polysilicon 

process [20] that results in gorgeous parts with straight 

smooth sidewalls. 

For several dollars, Murata sells a vibrating beam gyroscope 

with a piezoelectric readout. Since stability is poor, 

high-pass filtering is recommended. This gyro has been 

applied to vibration control problems such as camera and 

camcorder stabilization. O-Navi (formerly Gyration) is 

selling sample quantities. [21] Crossbow Technology and 

Cloud Cap Technology, Hood River, Oregon, deliver sixaxis 

systems based on Analog Devices’ inertial sensors. 

Other gyro manufacturers include L-3, Panasonic, and 

Samsung. [22],[23] Although mentioned on their web sites, 

little is known about these angular rate sensors. Imego, 

Sweden, [24] produces small numbers of sensors. Kionix, [25] 

Ithaca, NY, and Microsensors, a subsidiary of Irvine 

Sensors, advertise automotive-grade MEMS gyroscopes. 

SensoNor will ship their SAR10 automotive-grade angular 

rate sensor on short notice. [26] 

This paper’s unique contributions include: 1) analysis 

and tolerances required to realize antiparallel tuningfork 

motion; 2) two-degree-of-freedom model of instrument 

dynamics, including fluid and mechanical cross-axis 

couplings; 3) force and fluid coupling models, which 

dictate evacuated packages for better performance units; 

and 4) mechanical quadrature models that have led to laser 

trimming. 

When discussing performance, most published work on 

MEMS angular rate sensors focused on z-axis gyros, which 

sense rate perpendicular to the substrate, and emphasized 

wide bandwidth resolution. For z-axis gyros, nonideal 

suspension geometries were studied in References [27] and 

[28]. More recently, the University of California, Irvine, has 

considered z-axis gyro scale-factor variation with frequency 

and temperature. [29],[30] 

Description of Honeywell/Draper tFG 

The Draper/Honeywell TFG is shown in Figure 1. This 

sensor was designed to achieve the highest performance 

consistent with costs that are low compared with 

traditional mechanical sensors. The gyro consists of 

two perforated proof masses supported by a system of 

suspension elements. The suspension and proof masses 

are doped crystalline silicon anodically bonded to a 

Pyrex or glass substrate at the suspension beam anchors 

and at the comb structures. [31],[32] Curling from etch 

stop doping gradients is avoided by annealing silicon 

diffused with boron or by employing uniformly grown 

silicon-on-insulator. The glass substrate precludes onchip 

electronics; however, the high resistivity reduces 

Error Sources in In-Plane Silicon Tuning-Fork MEMS Gyroscopes 43

stray capacitance, which mitigates the need for on-chip 

circuitry. (With silicon wafers, bond pads are isolated from 

the conducting substrates by thin dielectric layers so that 

high stray capacitance limits performance. With on-chip 

circuits, bond pads and stray capacitance are avoided.) 

Sense 

Plate 

Torsion 

Beam 

Sense 

Electrode 

Base Beam Anchor 

(a) 

SPO SPO 

Drive 

Beam 

Proof 

Mass 

Anchor Base Beam 

LM LS MPO 

RS RM 

Figure 1. The Draper/Honeywell TFG mechanism. In 1(b) 

and 1(c), silver is metal, diagonal lines indicate 

silicon attached to glass, and white indicates 

suspended silicon. Electrical contact pads are 

right motor drive (RM), right sense electrode 

(RS), motor pickoff (MPO), left sense electrode 

(LS), left motor drive (LM), and sense pick off 

(SPO). 

On either side of each proof mass are interdigitated 

combs. [33] The outer combs (left and right motor in Figure 

1) are used for electrostatically driving the proof masses 

antiparallel to the substrate in the x direction. The inner 

combs (motor pickoff in Figure 1) sense the drive motion 

and are typically biased to 5 Vdc through an op amp that 

senses charge traversing the comb gap. As described in “The 

Fundamental Dynamics of Oscillating Coriolis Sensors” 

44 Error Sources in In-Plane Silicon Tuning-Fork MEMS Gyroscopes 

(b) 

Motor Pick Off 

Substrate 

W I Input Rate 

(c) 

y 

x 

Mass Motor 

Sense Electrode 

Proof 

Mass 

section, rotation about the in-plane z-axis induces Coriolis 

acceleration, which deflects the proof masses in opposite 

directions perpendicular to the substrate. Beneath the 

plates are deposited metal electrodes that are excited with 

dc voltages of opposite polarities. The right sense plate (RS 

in Figure 1) is typically excited with 5 V and the left sense 

plate (LS) with -5 V. Differential proof mass motion induces 

electrical currents in the structure that flow through the 

suspensions and sense pickoff (SPO, Figure 1) into a 

preamplifier whose input contains the input angular rate 

modulated by the drive frequency. 

With drive resonant frequencies from 10 to 20 kHz, these 

gyroscopes are relatively stiff with suspension stiffnesses 

greater than 100 N/m. With 3-µm gaps, mechanical spring 

force of 300 µN is available to overcome sticking; nevertheless, 

care in etching and release, in electronic excitation, 

and mechanical handling is required. 

As detailed below, the challenge is to obtain excellent 

performance in a device where the sensitivity to angular 

rate is small. Obstacles include manufacturing tolerances 

and the relatively large magnitudes of non-Coriolis forces 

and electrical drive and excitation signals. 

Mode Ordering 

A first challenge is designing the angular rate sensor’s 

dynamic eigenfrequencies. If one considers the TFG proof 

masses (Figure 1) rigid and the suspension beams without 

mass, 3 rotations and 3 translations times 2 masses imply at 

least 12 dynamic modes. For advanced designs, proof mass 

compliance and suspension modes add further considerations. 

The TFG is designed so that the lowest frequency 

modes are generally: 1) drive or tuning fork, 2) translation, 

3) sense, and 4) out-of-plane. In the tuning-fork mode, the 

proof masses move antiparallel to the substrate. One usually 

attempts to excite this mode through the electrostatic motor 

drive. Similar proof mass amplitudes are the design goal. 

The drive frequency is designed for 10-20 kHz to reduce 

vibration and acoustic effects. For the translation mode, 

the proof masses move parallel to the substrate. Because 

the drive combs are controlled to apply forces in opposite 

directions, translation should not be excited by electrostatic 

drive; however, translation is excited by linear acceleration. 

To ensure tuning-fork operation despite beam width tolerances, 

the in-plane translation frequency is usually set 10- 

15% or more away from the drive frequency. 

The sense mode has the two proof masses moving away 

or toward the substrate in opposite directions. This could 

also be a rotation about their common center. For good 

gain, the sense eigenfrequency is set 5-15% away from the 

drive. While higher gain can be achieved at smaller separation, 

small variations in the resonant frequencies result in 

larger fractional changes of scale factor. When the out-ofplane 

mode is excited, the two proof masses move together 

perpendicular to the substrate. It is important that the lowest 

modes do not fall close to one another and that higher order 

modes are not integral multiples of the basic four.

Obtaining ±2% sense-drive frequency separation tolerance 

is challenging. The mechanical design is done using 

modal analysis in finite-element calculations. The tolerance 

required is estimated by noting that the beam mass 

is small compared with that of the proof mass. As a first 

approximation, stiffness is determined by beam bending 

(more detailed analyses include torsion elements) so that 

the sense resonant frequency depends on the beam thickness 

as w1/2t3/2, while the drive resonance depends on the 

beam width as t1/2w3/2 . For a fixed thickness, the frequency 

separation is proportional to the beam widths. With greater 

detail, the frequency separation is still strongly determined 

by tolerances on the beam width and thickness. In the 

dissolved wafer process [31] used for the Draper/Honeywell 

TFGs, the beam width and thickness are determined in 

independent steps. The thickness is determined by boron 

diffusion or by purchased silicon-on-insulator wafers. The 

beam widths are set by masks and deep reactive ion etching. 

Typical beam widths are 10 µm. Achieving 2% accuracy in 

frequency separation requires 0.2-µm absolute accuracy of 

the beam widths. This accuracy challenges the tolerances 

on masks and requires great control of deep etching. 

Consider separation of the in-plane translation and drive 

or tuning-fork mode where the proof masses translate 

in parallel but opposite directions. Tuning-fork motion 

is desired to common mode reject in-plane linear accelerations 

and to reduce damping forces. With tuning-fork 

operation, the proof masses move in opposite directions so 

that the base beam (Figure 1) remains essentially stationary, 

and only small shear stresses are transmitted through 

the anchors to the substrate. With no anchors bending, 

energy is not transmitted or radiated to the substrate so 

that a high mechanical quality factor, a precursor to low 

force coupling (see next section), is attained. The tuningfork 

eigenfrequency depends only on the suspension beams 

from the proof mass to the base beam (Figure 1). With 

only a single proof mass, acceleration near drive frequency 

would alter the proof mass velocity and appear directly as 

a scale-factor error in (4). For order of magnitude common 

mode rejection, the driven amplitudes of the two proof 

masses should match to 10%; that is, the common mode 

motion or translation mode should be 5% of the individual 

proof mass motion. 

A lumped parameter, two-mass three-spring model for 

drive-translation motion is shown in Figure 2. Derived in 

Appendix A, the translation is related to the tuning fork or 

differential motion by: 

where 

k = nominal stiffness of beam from proof mass to base 

beam 

Dk = stiffness deviation from nominal (k1 = k + Dk/2, 

(1) 

k 2 = k - Dk/2) 

Dx = differential proof mass motion (x 1 – x 2 ) 

Sx = translation motion (x 1 + x 2 ) 

w H = eigenfrequency of hula (in-plane translation) 

mode 

DF = F 1 – F 2 = differential force (excites tuning-fork 

mode) 

s = Laplace transform of d /dt = jw D 

F 2 

Figure 2. Lumped parameter model of in-plane dynamics. 

Where the tuning-fork beams (from proof mass to base 

beam) largely determine the drive resonance, the translation 

mode also depends on the anchor beams (from 

anchors to base beam). Smaller differential stiffness and 

larger drive-translation frequency separation excites translation 

less. The stiffness depends on beam width cubed. 

Assume that the beam widths differ by 1% for the right 

and left proof masses, the differential stiffness is 3%. With 

the translation frequency 90% of the drive frequency, the 

translation motion is 6.4% of the tuning-fork motion. The 

beams must match to 0.1 µm (see earlier portion of this 

section). Achieving good separation often requires that the 

anchor beams be thinner than the tuning-fork beams. If the 

anchor beams are thick and rigid, the base beam is attached 

to the substrate and the proof masses move independently; 

that is, the drive and translation modes are identical. These 

thin beams present challenges and often approach the limits 

of micromachining capability. 

Fundamental Dynamics of Oscillating Coriolis sensors 

To understand TFG performance, consider a model that 

includes only the sense and drive modes. As shown in the 

previous section, the drive motion can often be considered 

separate from the translation (hula) modes. With only 

linear terms considered, the drive and sense axis dynamics 

are described by second-order spring-mass systems with 

coupling between modes: 

Drive 

Sense 

m 2 

Proof 

Mass 

x 2 x b x 1 

b 2 

k 2 

k b 

b b 

m b 

Base Beam 

Proof 

Mass 

where 

m = mass of one proof 

d,s = subscripts that indicate drive and sense axes, 

respectively. 

k 1 

b 1 

Error Sources in In-Plane Silicon Tuning-Fork MEMS Gyroscopes 45 

m 1 

F 1 

(2) 

(3)

= damping 

k = stiffness. Mostly mechanical with modifications 

by electrostatic forces 

kds = quadrature coupling. The drive axis suspension 

force coupling into the sense axes 

bds = in-phase damping ‘surfboard’ coupling to sense 

axis 

x = motion along drive axis (parallel to substrate) 

y = motion along sense axis (normal to substrate) 

s = Laplace transform of d /dt 

Fd = motor drive force applied by the outer combs in 

Figure 1 

WI = slowly varying input rate 

a = drive force coupling to sense axis 

Q = quality factor 

From (2) and (3), another challenge emerges. The driving 

force as well as the drive axis suspension force and drive 

axis damping are coupled into the sense axis. With good 

design, these forces should be small compared with the 

Coriolis Force . 

For low-frequency angular rate inputs, the desired output 

is the angular rate modulated by the drive frequency. As 

shown in the electrical circuit of Figure 3, the proof masses 

are the negative input of a high input impedance, highgain 

operational amplifier whose input node is at virtual 

ground. The feedback resistor is large so that it does not 

affect the output at the gyro’s drive frequencies. From (3) 

and Figure 3, the preamplifier output is given by (Appendix 

B): 

where 

Vo = output of preamplifier 

Vs = bias voltage (plus and minus applied to right and 

left sense plates in Figure 1) on sense electrodes 

(5 V, example values are given in parentheses) 

Vc = coupling (drive feedthrough) 

VN = preamplifier input voltage noise (10-8 V/ ) 


(4) 

Cfb = feedback capacitor about the sense axis preamplifier 

(2 pF) 

Cs = total of sense capacitors (2 pF) 

CN = preamplifier input capacitance to ground (5 

pF) 

Cc = coupling (undesirable capacitor) to virtual 

ground (preamplifier input) 

dCs /dy = differential change of sense capacitors with y 

motion (2 pF/3 µm) 

SC = sum of all capacitors attached to the virtual 

ground. Includes strays, working, feedback, 

and amplifier capacitors (12 pF). 

wd = drive mode undamped natural frequency 

(20 kHz x 2 prad/s) 

w s = sense mode undamped natural frequency 

(22 kHz x 2 prad/s) 

x o = amplitude of drive motion (10 µm zero-to-peak) 

Fs = cross coupling forces acting along the sense 

direction (B-6) 

q = phase shift through sense dynamics (B-6) 

Proof 

Mass 

C c Cs/2 C s /2 

V c -V s V s 

C N 

Figure 3. Circuit diagram for sense preamplifier analysis. 

In (4), it is assumed that the proof mass motion is driven 

so that the displacement is a sinusoidal function of time. 

The rate signal, the Coriolis term, is in phase with the 

proof mass velocity, i.e., in quadrature with the proof mass 

position. For the sample parameters above, the gyro scale 

factor at the preamplifier output is 1.3 mV/rad/s. With a 

field effect transistor (FET) preamplifier whose input noise 

at drive frequency is 10 nV/ , the rate equivalent noise 

is 10 deg/h/ . Attaining the theoretical noise limit is a 

challenge discussed further in the “Electrical Coupling” 

section. 

Because of the sense-drive frequency separation and high 

sense-axis quality factor, the damping term is omitted in 

the denominator of (4); therefore, gain does not depend 

on damping. High resonant frequencies are desired to 

remove the gyro’s sensitive frequencies from acoustic 

noise and vibration and to permit isolators that allow 

adequate bandwidth. For a fixed sense-plate bias, higher 

sensitivity is achieved by lowering the resonant frequencies 

and/or by decreasing the separation between sense 

and drive mode. Drive frequencies of 10-25 kHz and 

sense-drive mode separations of 5-15% have worked well 

for MEMS TFGs. At baseband, the transfer function of 

output voltage to rate input has a lightly damped peak 

at the frequency separation. Placing the separation at 1-2 

kHz allows a 100-Hz bandwidth, which adequately filters 

R fb 

V N 

C fb 

– 

+ 

V R 

V o 

Output 

Voltage

the undamped peak. If the frequency separation is small, 

the scale factor becomes sensitive to small variations in 

resonant frequencies (4). 

Demodulation (Figure 4) multiplies the output (4) by 

sin(wdt+j), a signal in-phase with the drive velocity. 

The output after demodulation and low-pass filtering is 

(Appendix B): 

(5) 

where 

Gac = gain before the demodulator 

VB = bias voltage in dc section often caused by amplifier 

offset voltages. 

dem = demodulation operation. Frequencies near the 

demodulation frequency are transferred to baseband 

by the sin(wdt+j) demodulation 

j = small phase shift between rate signal in sense 

chain and demod reference 

Drive 

Force 

Drive Axis 

Dynamics 

Self-Drive Oscillator Loop 

Velocity Velocity 

Signal 

2mWI Output 

Noise 

Other 

Forces 

S 

Sense Axis 

Dynamics S 

Electrical 

Comp. 

ac 

Gain 

Sense Axis Chain 

Figure 4. TFG electrical block diagram. 

In (5), small angle approximations for the angles q and 

j were applied. The ac gain, typically 5-20 V/V, and the 

low-pass filtering blocks are shown in Figure 4. This low 

pass filter, typically 50-100 Hz, sets the gyro’s bandwidth. 

Feedthrough terms (5) are extremely important. The 

demodulation function dem emphasizes that extra voltages 

in phase with drive velocity appear directly as dc bias errors 

in the TFG. Components in quadrature to drive velocity 

are greatly reduced at the dc output; however, mechanical 

and electric phase shift error causes quadrature terms 

to appear as in-phase bias. Individual challenges and their 

implications on gyro construction are discussed in the next 

section. 

X 

Filter and 

dc Gain 

Indicated 

Rate 

error Mechanisms 

Force-Related Errors – The Impetus for Evacuation 

Vacuum packaging is needed to reduce the required motor 

force and the voltage required to drive the motor. From (3), 

the motor force couples into the sense axis. For reasonable 

scale factor, large drive amplitude is desired so that the 

drive axis is operated at resonance; that is, the motor force 

is in phase with the drive velocity. When the interdigitated 

combs are over a ground plane, lift forces are exerted. [33] 

Derived in Appendix C, the erroneous estimated angular 

rate can be calculated from: 

For a single set of combs, the coupling coefficient a is 

of the order of 0.3. [33] Because the left and right motors 

behave similarly, this is common mode coupling. Since 

both outer combs cause lift and since the sense plate excitation 

is selected to detect differential motion, the differential 

coupling determines the gyro bias. The coupling 

coefficient depends strongly on vertical misalignment (the 

disengagement) of the moving and stationary combs. [33] 

With a 20-kHz drive frequency and 100,000 quality factor, 

the erroneous common mode angular rate is 0.2 rad/s. The 

differential magnitude is typically an order of magnitude 

smaller. Because damping changes by a factor of three over 

operating temperature, thermal compensation is usually 

employed; nevertheless, the absolute tolerances and stability 

of the comb disengagements must be held very closely 

to achieve tactical performance. 

In addition to the electrostatic force coupling, hydrodynamics 

couple drive force into sense force. Described by 

lubrication theory, the fluid coupling is described in detail 

with closed-form solutions in Reference [34]. Once the 

coupling coefficient is calculated, (6) can be used to estimate 

the impact on estimated angular rate. Evacuation 

and pressure relief holes are required for acceptably low 

effects on in-phase bias. Perforated designs such as Figure 

1 result in hydrodynamic lift that is smaller than the electrostatic 

coupling. The perforations also assist cleaning and 

inspection. 

The random motion of the proof mass is dictated by Brownian 

motion. To achieve preamplifier limited performance, 

gas damping must be reduced by evacuation so that the 

principal damping is material and radiation through the 

anchors into the glass. 

Even if a vacuum is not required (as in an accelerometer), 

the small gaps and masses dictate hermetic sealing since 

humidity variation causes unacceptable variations in scale 

factor because of effective gap change. As temperature 

changes even with hermetic sealing, outgassing deposits 

material and changes the sense and motor gaps so that the 

scale factor is changed. 

To summarize, evacuation is required in high-performance 

gyros for the following reasons: 1) reduce the electrostatic 

Error Sources in In-Plane Silicon Tuning-Fork MEMS Gyroscopes 47 

(6)

drive force and, hence, coupling into sense axis force; 2) 

reduce hydrodynamic lift (surfboarding) effects; 3) maintain 

acceptable phase stability between sense and drive axes 

(the omitted damping in the denominators of (4) and (5)); 

4) render Brownian motion small so that wide bandwidth 

resolution is achieved; and 5) enhance resolution since low 

damping does not restrict sense-axis motion in (4) and (5). 

Low damping increases proof mass motion if shocks are 

applied. These effects are reduced by the two-mass design, 

which rejects common mode inputs, and modal frequency 

selection. The high resonant frequencies are above most 

shock spectra, which are often defined to a few kilohertz. 

With high resonant frequencies, shocks and acoustic 

inputs are reduced by suspension isolating the IMU. The 

sense axis baseband peak, which occurs at the drive-sense 

separation, typically 10 kHz, is greatly reduced by sense 

chain low-pass filtering. 

Mechanical Quadrature 

The drive axis is operated at resonance so that the stiffness 

and inertial forces in (2) cancel and the drive-axis response 

is dominated by damping; nevertheless, a relatively large 

spring force is being exerted. Because of manufacturing 

imperfections or tolerances, the mechanical stiffness force 

results in the cross-coupling term kds. A slender beam tries 

to bend along its principal axes of inertia. [35] If the principal 

inertias are not aligned with the drive and sense axes, 

an attempt to bend the beams in the x direction results in 

a y force. Consider the cross section of a simple suspension 

beam where the sidewalls are not cut vertical but at 

an angle q to form a parallelogram cross section as shown 

in Figure 5. For small sidewall angles q, the ratio of crosscoupling 

to in-plane force is given by: [36] 

where 

t = thickness of suspension beams and proof mass as 

defined in Figure 5 

w = nominal beam width as defined in Figure 5 

q = tilt of sidewalls 

t 

Y Axis (Substrate Frame) 

w a 


(7) 

Figure 5. Nomenclature for analyzing quadrature from 

beam sidewall angle. 

q 

X Axis 

Because the suspension consists of several beams rather 

than a simple cantilever, the mechanical quadrature is 3- 

10 times smaller than that calculated by (7). Equating the 

Coriolis term to the cross-coupled term as in Appendix C, 

the estimated input rate error from cross coupling is given 

by: 

Because the coupling is in-phase with drive position, the 

cross-coupled force term is in quadrature with the desired 

rate signal. With good demodulation (see “Mode Ordering”), 

little quadrature should appear in the indicated 

rate output. In a typical TFG, t/w = 2. Because of the two 

proof masses, the differential coupling between right and 

left masses is the principal concern. With sidewall slopes 

matched to 0.002 r (0.1 deg), a tight tolerance for vertical 

deep etching in silicon, the coupling ratio aQ is 0.008 

and the magnitude of the quadrature signal (8) is 502 rad/ 

s (108 deg/h). For tactical performance, the sheer magnitude 

of the possible quadrature signal presents major design 

challenges. In addition to dynamic range, small variations 

in demodulator phase lead to unacceptable bias shifts. 

The TFG handles quadrature by very careful micromachining 

and by applying a quad nulling loop [37] to reduce 

the quadrature signal injected into the sense channel. As 

shown in Figure 4, the sense axis output is demodulated 

into components in-phase and in quadrature with the 

desired input rate-drive velocity signal. The sense chain 

quadrature signal is nulled by applying a dc voltage bias to 

the drive combs in addition to the two frequencies motor 

drive. Because of limited available voltage, mechanical 

quadrature must be less than 50 rad/s for successful quad 

nulling. Because of the nulling loop, the sense chain does 

not require head room for the large mechanical quadrature. 

High-performance or as-etched quadrature larger 

than 50 rad/s requires mechanical trimming, a procedure 

described in Reference [36]. The difficulty of quadrature is 

that small imperfections lead to large quadrature; however, 

only small amounts of material must be removed for effective 

trimming. 

Electrical Coupling 

The drive voltages are typically 5 V. From (4) or (5), 100 

fF (Cc = 10-13 F) stray capacitance to the sense node results 

in an output voltage of 250 mV, equivalent to 200 rad/s 

(4 x 107 deg/h). Small coupling capacitance can lead to a 

sense change signal much larger than the desired angular 

rate resolution and to dynamic range issues. This coupling 

effect is mitigated by two-frequency operation and balanced 

drive. The coupling can occur at the combs or in the leads 

leading to the package or even in the electronics itself. 

For an electrostatic drive, the force is proportional to the 

voltage squared; thus, the drive force could be at the difference 

frequency between two input voltages. [37] Because 

the two frequencies can differ from the drive frequency 

(8)

at which demodulation is done, coupling effects from the 

motor to the sense are greatly reduced (5). Because the half 

frequencies are generally derived from the motor position 

signal, the motor drive must be designed carefully to make 

motor frequency signals small. 

Voltage squaring allows the motor to be driven with plus 

and minus voltages, which reduce the coupling into the 

sense chain. Because of amplitude mismatch (see “Mode 

Ordering”), the voltages must cancel for each proof mass so 

that layout and connections become more complicated. A 

bias is added to the motor drives to null mechanical quadrature 

signals and charge injected by the motor pickoff. 

For proper operation, the motor drives must also be 

isolated from the motor sense so that the drive oscillator 

loop locks onto the mechanical motion and not onto the 

half frequency signals. Considerations of dynamic range, 

motor loop oscillator, and stability dictate that capacitance 

be matched to 10 fF, a significant design and manufacturing 

challenge. This figure is supported by simulation and 

results of production units. 

Conclusion 

For TFGs, the phenomena that cause the principal errors in 

estimating angular rate were evaluated. To realize a working 

MEMS gyroscope, many design features must be done 

correctly. Design teams must converge quickly to a feasible 

solution or have sufficient resources to afford several iterations. 

The challenges overcome in realizing a high-performance 

MEMS gyro included: 1) geometric tolerances, 

2) attaining theoretical noise limits, 3) vacuum packaging, 

4) reduction of mechanical quadrature, 5) eigenfrequency 

location, 6) electrical coupling, and 7) thermal 

expansion effects. Precise suspension beam dimensions 

were required to maintain the desired ordering of modes 

and frequency separation to achieve beam symmetry for 

reasonable quadrature and to maintain comb disengagement, 

which causes vertical forces. Achieving acceptable 

quadrature required mechanical trimming and electrical 

feedback. Reaching theoretical noise limits required careful, 

symmetric layout of electrical leads, of electronics, and 

of the sensor itself to avoid coupling through unbalanced 

stray capacitance. Thermal expansion changes dimensions 

that change gyro performance; for example, comb engagement 

alters sense axis force, and, hence, instrument bias, 

and sense gap alters scale factor. Alternatives for overcoming 

the above challenges are presented by introducing the 

Analog Devices and BEI angular rate sensors. 

Draper used the considerations and analyses presented 

here in developing the TFG technology Honeywell has 

applied to its navigation systems. After a decade of excellent 

test data, production quantities are now being realized. 

In 2004, several hundred systems were delivered for 

mainly military applications, such as artillery shell and 

mortar shell guidance. Gyro noise is 5-10 deg/h/ with 

bias and scale factor repeatability over temperature and 

turn off better than 30 deg/h and 400 ppm, respectively. 

Raw, uncompensated thermal sensitivities are 10 deg/h/°C 

and 250 ppm/°C. 

appendix a. Derivation of translation Mode from 

Differential Force 

The relation for translation mode versus differential mode 

(1) is derived. From Figure 2, consider only motion parallel 

to the substrate. Neglect damping and apply Newton’s 

law to proof masses 1 and 2 and to the base beam: 

F1 = m1s2x1 + k1 (x1 – xb ) (A-1) 

F2 = m2s2x2 + k2 (x2 – xb ) (A-2) 

0 = (mbs2 + kb )xb – k1 (x1 – xb ) – k2 (x2 – xb ) (A-3) 

where 

k = stiffness of extension spring 

m = mass 

x = displacement of mass 

1,2,b = subscripts indicating proof mass 1, proof mass 2, 

or base beam 

s = Laplace transform of d /dt = jwD Add (A-1) and (A-2) to obtain the translation equation: 

(A-4) 

where 

Dk = stiffness deviation from nominal (k1 = k + Dk/2, 

k2 = k - Dk/2) 

Dm = mass deviation from nominal (m1 = m + Dm/2, 

m2 = m - Dm/2) 

Dx = differential proof mass motion (x1 – x2 ) 

Sx = sum of translation motion (x1 + x2 ) 

DF = F1 – F2 = differential force (excites tuning-form 

mode) usually applied by electrostatic comb 

drive 

SF = F1 + F2 = sum of forces (excites translation). Loads 

caused by substrate acceleration along the drive 

direction are included here. 

Subtract (A-2) from (A-1) to obtain the differential drive 

mode equation. 

(A-5) 

With perfect construction, the translation (A-4) includes 

the base motion while the differential motion (A-5) is free 

of base motion. Reorder (A-3). 

(A-6) 

With a large number of teeth, the differential drive force is 

much larger than the sum. The base beam mass is much 


less than the proof masses. Therefore, set m b and SF to 

zero and solve (A-4) through (A-6) simultaneously for Sx, 

Dx, and x b . 


(A-7) 

where w H = eigenfrequency of hula (in-plane translation) 

mode 

= 

w d = drive frequency = 

Because of their larger lateral dimensions, proof masses 

match more closely than the spring stiffnesses; therefore, 

Dm in (A-7) was set to zero to obtain (1). 

appendix B. Derivation of sense Preamplifier Output 

The sense axis preamplifier output (4) and the demodulated 

output (5) are derived. Solve (2) and (3) simultaneously 

for the drive and sense axis positions x and y. Assume 

that fluid and suspension cross couplings b ds and k ds , the 

Coriolis coefficient 2mW I, and the force coupling a are 

small. Because is motion is driven by small terms, the sense 

position becomes a small term. Neglecting the products of 

small terms, the drive and sense positions are determined 

by: 

(B-1) 

(B-2) 

where s = Laplace transform of time derivative d/dt 

Because the drive oscillator loop requires that the drive 

loop operate at resonance, the drive position and force 

are sinusoids once steady-state operation is achieved; that 

is: 

x(t) = xocos(wdt) (B-3) 

Fd(t) = -bdxowdsin(wdt) (B-4) 

Since the sense mode resonant frequency is typically 10% 

different from the drive resonant frequency, the damping 

can often be neglected in determining the steady-state sense 

position magnitude. Solve (B-2) with (B-3) and (B-4). 

where 

q = phase shift through sense dynamics 

(B-5) 

= 

The hydrodynamic lift and the drive force coupling are inphase 

with the desired rate signal, while the suspension 

force coupling is out of phase. The sense position (B-5) can 

be written as: 

(B-6) 

where 

Fs = force acting in sense direction 

Fs = (abd – bds )xowdsin(wdt + q) + kdsxocos(wdt + q) 

The sense preamplifier output is determined from the 

circuit diagram of Figure 3. The sense plates below the 

proof masses are biased with opposite voltages (Figure 1) 

so that antiparallel vertical motion is detected. Because of 

the amplifier’s high gain, the preamplifier input, which is 

wired directly to the proof masses, is at virtual ground. 

Because the feedback resistor Rfb is large, the resistor 

and its Johnson noise are small effects at the gyro drive 

frequency wd . 

(B-7) 

Inserting (B-6) into (B-7) yields (4). Demodulation (Figure 

4) multiplies the output (4) by sin(w d t+j), a signal inphase 

with the drive velocity. High-frequency content is 

removed by low-pass filtering so that the output after ac 

gain and demodulation is described by (5), which includes 

a bias voltage from amplifier offsets in the dc chain. 

appendix C. Derivation of In-Phase Bias error from 

Force Coupling 

Equation (6) for calculating the in-phase bias caused by 

force coupling is derived. Since the TFG is operated at the 

drive resonance, the drive force amplitude on one proof 

mass is given by: 

(C-1) 

To calculate the angular rate errors, the undesired sense 

axis forces F s are compared to the Coriolis acceleration 

2mW I w d x o ; that is, the estimated rate is calculated 

from: 

(C-2) 

The undesired force is the drive force multiplied by the 

coupling coefficient a F . Inserting aF d from (C-1) into (C-2)

esults in (6). Because both the coupled and Coriolis forces 

act on the sense axis dynamics, the frequency separation 

denominator of (4) does not appear in (C-2). 

appendix D. In-Plane Quartz Gyroscope 

The quartz rate sensors (QRS) reached the market in the 

late 1980s, a decade before silicon MEMS devices were 

developed. The QRS has been a very successful product; 

therefore, a comparison with silicon TFGs is instructive. 

A typical Systron Donner/BEI QRS is shown in Figure 6. 

Per References [17] and [18], the actual designs differ 

depending on applications, which range from tactical to 

automotive. The H-shaped sensing mechanism is made of 

piezoelectric quartz, a significant variation from the electrostatically 

silicon gyros. Electrodes are deposited so that 

the upper tines are driven as a tuning fork with antiparallel 

motion in the substrate plane. Because of symmetric 

construction and mechanical coupling, the lower tines 

oscillate at the drive frequency, although they are not 

excited electrically. When the substrate is rotated about an 

axis parallel to the tines (Figure 6), the drive tines move 

into and out of the plane in response to the Coriolis acceleration, 

deflections that are coupled into the lower, sense 

tines. The sense electrodes are designed, deposited, and 

wired to sense the out-of-plane sense motion. 

Drive 

Tines 

Input Rate Rotational Rate 

DC Voltage 

Output 

Drive 

Oscillator 

Pickup 

Tines Pickup 

Amplifier 

(a) 

(b) 

Amplifier 

Amplifier 

Reference 

Demodulator 

Figure 6. BEI quartz rate sensor: (a) sensing mechanism, 

(b) schematic of operation. [18] 

Because of the piezoelectric material, drive and detection 

signals are at the same frequency for constant rate inputs, 

and gaps around the moving elements are much larger than 

the 1-4 µm typical of the electrostatically-driven devices. 

Silicon micromachining’s deposition, doping, and wafer 

bonding techniques are not available in quartz; therefore, 

quartz parts are generally limited to wafer thickness, which 

is greater than 100 µm (silicon parts are 5-20 µm thick or 

several hundred micron). 

The greater thickness and the required proximity of in- and 

out-of-plane eigenfrequencies results in moving elements 

larger than those of the silicon MEMS devices. Drive oscillation 

at 9 to 17 kHz dictates the length of the tines, while the 

continuous beams and the number of tines dictate that the 

tines and tip masses must be shaped carefully. [18] Because 

the wafers are 100 µm thick, the wafers are much smaller 

than those used in silicon processing. The combination of 

small wafers and large die tend to make the projected QRS 

costs higher than those for silicon rate sensors. Because of 

the thick part and large air gaps, sticking should not be an 

issue for the QRS. Because of the thicker parts and larger 

gaps that result in lower damping, it is possible that the 

QRS can be sealed at higher pressures than the TFG and 

still demonstrate low Brownian motion noise. 

The quartz’s etching characteristics are not as controlled 

as those of silicon because of the fundamental nature 

of quartz crystallographic properties and the etchants. 

The etching results in sidewalls (see “Error Mechanisms: 

Mechanical Quadrature”) that require each part, including 

automotive, be trimmed. [18] Trimming has been done by 

the addition of mass and by laser removal, a process that 

has been highly automated. For high-performance sensors, 

the level of quadrature trimming is suspected to be quite 

tight because the linear piezoelectric drive does not offer 

the possibility of quadrature nulling discussed in the “Error 

Mechanisms: Mechanical Quadrative” section. 

With piezoelectric operation, both the drive signals and the 

sense output are at the same frequency for no rate input. In 

electrostatically operated silicon devices, the drive voltages 

can be at different frequencies from the sensed output (see 

“Error Mechanisms: Electrical Coupling”). For the QRS, the 

sense and drive electrodes are physically separated in the 

H structure so that coupling within the sensor should be 

small; nevertheless, controlling stray capacitance is challenging. 

BEI has demonstrated proprietary electronics [18] 

that enable tactical performance so that other stray paths 

have been controlled. 

appendix e. analog Devices Out-of-Plane Gyroscopes 

Analog Devices began their gyro development with the 

ground rules that the instrument should be inexpensive 

but should satisfy automotive applications. To minimize 

expense, Analog’s accelerometer CMOS and polysilicon 


process was mandated. In the mid-1990s, the process 

focused on 2-µm thick suspended parts. Based on performance 

considerations, Analog has moved to 4-µm thick 

suspended polysilicon parts. [38] The 4-µm thickness 

results in smaller moving parts, shorter beams, and smaller 

deflections than for the larger TFGs. To incorporate onchip 

circuitry, the substrate must be silicon. The moving 

elements, wire runs, and bonding pads are isolated from 

the conducting silicon substrate by an oxide layer. 

As shown in Figure 7, the gyro mechanism consists of two 

independent mechanical structures. [38] For each structure, 

the inner member is driven and sensed electrostatically. The 

sensing frame supports the driven member. An angular rate 

about an axis perpendicular to the substrate moves the driven 

mass along the sense direction (Figure 7), which is parallel to 

the substrate plane. As discussed below, the suspension is 

Coriolis Sense Fingers 

Coriolis Sense Fingers 

Drive Direction 

Inner Frame 

Resonating Mass 

Velocity Sense Fingers 


(a) 

(b) 

Drive Fingers 

Self Test 

Figure 7. Mechanism for Analog Devices ADXRS angular 

rate sensor: (a) photomicrograph, [41] (b) sketch 

of one proof mass assembly. [42] 

designed so that the sensing frame does not move in the drive 

direction, but follows the proof mass in the sense direction. 

Electrostatic combs detect the frame position. 

Eliminating trimming to reduce quadrature was a dominant 

decision in ADXRS design. [38]-[42] With crab leg or folded 

beam suspension, different beam stiffness can cause senseaxis 

motion when driving the proof mass. [40] Because this 

motion is in phase with position, it is in quadrature to the 

desired rate-induced motion. The ADXRS beam widths are 

1.7 µm, and width tolerances are 0.2 µm so that quadrature 

reduction was a major design goal. [38] Straight beams 

between the sense and drive elements (Figure 7) result in 

very little sense-axis motion. The beams have stress relief 

at their ends (not shown in Figure 7) to reduce longitudinal 

stresses from polysilicon thermal expansion and from 

drive motion. Although Analog has not employed it, a fine 

quadrature trim is possible by fingers excited to exert a 

sense force that is modulated by the drive motion. [43] 

In the ADXRS, both the sense and drive motions are parallel 

to the substrate’s plane; thus, all critical dimensions are 

done in one masking and etching operation. If the polysilicon 

thickness is off, all frequencies move together so 

that mode ordering is maintained. While the proof mass 

is driven at 7-µm amplitude, the sense motion for angular 

rate is roughly 10-10 m/rad/s, [38] an order of magnitude 

lower than for TFGs. This smaller motion is attributed to 

smaller drive amplitude, the fact that the drive mass must 

also drive the additional sense mass, and 20 to 30% separation 

of sense and drive resonant frequencies. The greater 

separation is consistent with 2-µm beam width compatible 

with 4-µm thickness and the resulting proof mass and 

suspension dimensions. 

The gyro consists of two mechanically independent mechanisms 

(not tuning forks, see “Mode Ordering” section) 

whose drive frequency is roughly 15 kHz and whose 

quality factor is 45. [38 ] The units are electrically crossconnected 

[42] so that the proof masses move antiparallel 

to common mode reject linear acceleration. To achieve 

common mode rejection with a Q of 45, the two drive 

resonant frequencies should be within 1% of each other. 

If the moving drive teeth are not centered with respect to 

the stationary teeth (i.e., the entire proof mass is moved 

relative to the stationary combs), a large coupling to drive 

force results. The coupling of drive force to sense-axis 

effects are described in (3). Since the drive force is large 

because of the high damping and since the drive force is 

in phase with the drive velocity and, hence, the Coriolis 

acceleration, the proof mass must be centered to very tight 

levels. 

With 1.7-µm wide beams, achieving the geometric control 

for sense drive frequency separation, matching drive 

frequencies, and centering the combs is challenging.

The ADXRS is hermetically sealed at 1 atmosphere. 

Because of the resulting damping, noise is limited by 

Brownian motion. [38] To achieve drive amplitude, the 5-V 

supplies must be boosted to approximately 12 V. Damping 

adds phase shift between sense and drive axes. Electronics 

design and increasing separation between sense and 

drive frequencies reduce the effect of this additional phase 

shift. The resulting damping renders the ADXRS tolerant 

of operating shock. 

The ADXRS relies heavily on its on-chip electronics to overcome 

the small size and low scale factor of the mechanical 

parts. The sense displacement per rate input is 10% and 

the capacitance variation is 1% of the 20-µm thick TFGs. 

Analog measures displacement resolution similar to the 

TFGs, but with much smaller capacitors. 

acknowledgments 

We gratefully acknowledge Draper Laboratory’s financial 

support and the dedicated work of Draper’s silicon fabrication 

and packaging groups. John Geen of Analog Devices 

offered fruitful insight into the ADXRS operation. Thanks 

to Beverly Tuzzalino for final preparation of the manuscript 

and to Neil Barbour for proofreading and discussions. 

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Conference on Modeling and Simulation of Microsystems 

(MSM), San Juan, Puerto Rico, April 22-25, 2002. 

[29] Acar, C. and A.M. Shkel, “Nonresonant Micromachined Gyroscopes 

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[30] Painter, C.C. and A.M. Shkel, “Structural and Thermal Modeling 

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U.S. Patent No. 5,349,855, September 27, 1994. 

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Micro-Machined Structures,” JMEMS, Vol. 14, No. 4, 

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Micromechanical Devices, U.S. Patent No. 6,571,630 

B1, June 3, 2003. 

[37] Ward, P., Electronics for Coriolis Force and Other Sensors, 

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[38] Geen, J.A., S.J. Sherman, et al., “Single-Chip Surface Micromachined 

Integrated Gyroscope with 50 °/h Allan Deviation,” 

IEEE Journal of Solid State Circuits, Vol. 37, No. 12, 

2002, pp. 1860-6. 

[39] Geen, J.A. and D.W. Carow, Micromachined Devices, U.S. 

Patent No. 6,684,698 B2, February 3, 2004. 

[40] Geen, J.A. and D.W. Carow, Micromachined Gyros, U.S. Patent 

No. 6,122,961, September 26, 2000. 

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Gyroscope,” Analog Dialogue, Vol. 37, No. 1, January 

2003, pp. 12-5. 

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54 Error Sources in In-Plane Silicon Tuning-Fork MEMS Gyroscopes

(l-r) Anthony Kourepenis 

and Marc Weinberg 

bios 

Marc Weinberg is a Laboratory 

Technical Staff Member. He has 

been responsible for the design 

and testing of a wide range 

of traditional micromechanical 

gyroscopes, accelerometers, 

hydrophones, microphones, angular displacement sensors, chemical sensors, and biomedical devices. He holds 25 patents with 

12 additional in application. He served in the United States Air Force at the Aeronautical System Division, Wright-Patterson 

Air Force Base during 1974 and 1975, where he applied modern and classical control theory to design turbine engine controls, 

and at the Air Force Institute of Technology, where he taught gas dynamics and feedback control. He has been a member of the 

American Society of Mechanical Engineers (ASME) since 1971. Dr. Weinberg received BS (1971), MS (1971), and PhD (1974) 

degrees in Mechanical Engineering from MIT where he held a National Science Foundation Fellowship. 

Anthony Kourepenis is currently Associate Director of the Tactical Programs Office at Draper Laboratory. He has been principally 

involved with the design of solid-state inertial instruments and has been the technical lead for several successful instrument and 

systems design, development, and demonstration programs. His diverse background includes experience in both hardware and 

software design, applied physics, data acquisition and analysis, sensor, instrument, and systems design, electronics architecture 

development, test and evaluation, error modeling and interpretation, and signal processing. He holds six patents and has four 

pending. Dr. Kourepenis received BSEE (1988) and MSEE (1992) degrees from Northeastern University and an MSEM (1996) 

from Tufts University. 


56 

Model-Based Variational Smoothing 

and Segmentation for Diffusion 

Tensor Imaging in the Brain 

Mukund N. Desai, 1 David N. Kennedy, 2 Rami S. Mangoubi, 1 et al. 

Copyright © 2006 Humana Press, Inc. Published in Neuroinformatics, Vol. 4, No. 3, 2006, pp. 217-234 

abstract 

This paper applies a unified approach to variational smoothing 

and segmentation to brain diffusion tensor image data 

along user-selected attributes derived from the tensor, with 

the aim of extracting detailed brain structure information. 

The application of this framework simultaneously segments 

and denoises to produce edges and smoothed regions within 

the white matter of the brain that are relatively homogeneous 

with respect to the diffusion tensor attributes of choice. The 

approach enables the visualization of a smoothed, scaleinvariant 

representation of the tensor data field in a variety 

of diverse forms. In addition to known attributes such as 

fractional anisotropy, these representations include selected 

directional tensor components and, additionally associated 

continuous valued edge fields that may be used for further 

segmentation. A comparison is presented of the results of 

three different data model selections with respect to their 

ability to resolve white matter structure. The resulting 

images are integrated to provide a better perspective of the 

model properties (edges, smoothed image, etc.) and their 

relationship to the underlying brain anatomy. The improvement 

in brain image quality is illustrated both qualitatively 

and quantitatively, and the robust performance of the algorithm 

in the presence of added noise is shown. Smoothing 

occurs without loss of edge features due to the simultaneous 

segmentation aspect of the variational approach, and the 

output enables better delineation of tensors representative of 

local and long-range association, projection, and commissural 

fiber systems. 

Introduction 

Diffusion weighted and diffusion tensor magnetic resonance 

imaging (MRI) has come into widespread use over the 

past few years. This is mainly because of the unique view 

diffusion imaging provides of the microstructural details 

within the cerebral white matter in health and disease. As it 

represents a relatively new class of image data, the processing 

required for visualization and analysis of tensor data 

provides numerous new challenges. 

1 Control and Information Systems Division, Draper Laboratory, Cambridge, MA. 

2 Center for Morphometric Analysis and Massachusetts General Hospital (MGH)/MIT Athinoula A. Martinos Center 

for Biomedical Imaging, Department of Neurology, MGH, Boston.

The history and general descriptions of the standard methods 

for diffusion imaging are discussed in detail in recent 

reviews of the field. [1]-[3] Diffusion imaging has been used in 

a host of clinical and research application areas. [4]-[13] The 

ability to use diffusion tensor imaging (DTI) directionality 

and anisotropy to characterize the compact portion of 

discrete corticocortical association pathways in the cerebral 

white matter of living humans has been demonstrated and 

validated. [14] Identification and visualization of specific fiber 

tracts [15]-[24] and exploration of the potential to elicit information 

about functional specificity [25] have also been carried 

out. The wide variety of application areas, along with the 

fact that the novel in vivo data are obtainable in this fashion 

makes DTI a potentially powerful clinical tool. 

Compared with conventional MRI, however, DTI image 

acquisition is quite slow, due to the need to encode multiple 

different directions of diffusion sensitivity. This leads 

to practical tradeoffs in the use of DTI between acquisition 

time, diffusion sampling method, spatial resolution, and 

slice coverage. Partial volume effects are particularly problematic 

in DTI since competition of multiple different directional 

features within a voxel can render the resultant tensor 

not representative of the underlying anatomic structure. The 

development of methods that take optimal advantage of the 

diffusion data in light of potentially low signal-to-noise ratio 

(SNR) is an important objective for making DTI more clinically 

relevant. 

Prior work in regularizing or smoothing diffusion tensor 

fields include the work in Reference [15], where a Markovian 

model is proposed to track brain fiber bundles in the DTI 

data. Diffusion direction is applied to fiber tract mapping 

and smoothing in Reference [26], in which the total variation 

norm algorithm is applied to the raw data. Regularization 

of diffusion-based direction maps to track brain white 

matter fascicles is reported in Reference [21], in which the 

emphasis is on the use of prior information in a Bayesian 

framework, and in Reference [27], in which the paths of 

anatomic connectivity are determined based on the directionality 

of the tensor. A continuous field approximation 

of discrete DTI data has been applied in Reference [28] to 

extract microstructural and architectural features of brain 

tissue. Smoothing employing parametric patches has been 

applied in Reference [23] to three-dimensional (3D) scattered 

data that describe anatomic structure. 

In this paper, we present an algorithm for simultaneous 

smoothing or denoising and segmentation of diffusion 

tensor data. This algorithm smooths the image field within 

homogeneous regions, while at the same time preserves the 

edges of these regions at discontinuities by generating the 

associated edge fields based on user-selected tensor attributes. 

The smoothing and edge estimation are applied with 

respect to a user-selectable “mapping,” or models, of the 

input tensor data in order to emphasize specific properties of 

the tensor. Sample application of the algorithm is presented 

that demonstrates smoothing with respect to normalized 

tensor magnitude and principal eigenvector direction. In 

these examples, the identification of white matter anatomic 

structure is qualitatively enhanced and reduction of regional 

anisotropy variance is quantified. This reduction in variance 

is then shown to be robust in the presence of added noise. 

While demonstrated with respect to specific data models, 

this simultaneous smoothing and segmentation framework 

is general and opens a rich and versatile set of processing 

options to address the noisy, voxel-averaged sampling of 

DTI data. It also enables the selection of appropriate models 

of various physical characteristics of the diffusion tensor in 

cerebral white matter. Specific clinical objectives will dictate 

the optimal selection of “mapping” models and parameters 

for enhanced smoothing and segmentation and will be the 

focus of future studies. 

Materials and Methods 

Data Acquisition 

The sample data used in this paper used the following protocol: 

Siemens 1.5 Tesla Sonata, five sets of interleaved axial 

slices to provide 2 × 2 × 2 mm 3 contiguous coverage, singleshot 

echo-planar imaging (EPI) with six directional diffusion 

encoding directions, and a nonencoded baseline acquisition 

was performed with TR = 8 s, TE = 96 ms, averages = 12, 

number of slices = 12 per interleave, data matrix = 256 (readout) 

× 128 (phase encode), and diffusion sensitivity b = 568 

s/mm 2 . The total imaging time for the session was approximately 

45 minutes. The subject provided informed consent 

and was a 35-year old, right-handed male normal control 

from a study of schizophrenia. The Institutional Review 

Board of the Massachusetts General Hospital approved the 

study protocol. 

Computation of the Diffusion Tensor Attributes 

Once the diffusion tensor, g, is sampled, the magnitude (or 

trace) can be calculated to express the total (no directionality) 

diffusivity at the voxel location. The directionality of 

the diffusion is assessed by an eigen decomposition of the 

diffusion tensor 

where l i , s i , i = 1,…3 are the three eigenvalue-eigenvector 

pairs for the tensor with eigenvectors of unit magnitude. The 

largest eigenvalue and the associated eigenvector correspond 

to the major directionality of diffusion at that location. The 

fractional anisotropy fa [29] is a scalar measure that is often 

used to characterize the degree to which the major axis of 

diffusion is significantly larger than the other orthogonal 

directions. 

Specifically regarding brain imaging, to the extent that 

white matter fiber systems have homogeneous directionality 

at the spatial scale of the voxel size, these fiber systems 

Model-Based Variational Smoothing and Segmentation for Diffusion Tensor Imaging in the Brain 57

are expected to demonstrate significant anisotropy. More 

general eigenvalue/eigenvector-based scalar as well as vector 

and tensor features can be used to capture the underlying 

structure in the diffusion tensor image. 

We have developed a segmentation and smoothing approach 

that permits user selection among these (and other) features 

of the tensor image in order to capture the relevant underlying 

structural details. 

The Approach 

The core concept of the method is the simultaneous variational 

segmentation and smoothing formulation. Given 

an observed tensor field, g, the objective is to obtain 

two outputs: the smoothed tensor u, and edge field v. 

These outputs, respectively, represent the simultaneous 

smoothing and segmentation of the raw tensor data. The 

approach, shown schematically in Figure 1, makes use of 

the following: 

• A specified data fidelity model H(u, g). 

• A continuity model, f(u), that forms a basis for adaptively 

determining the regions of continuity within 

which smoothing is to take place. 

Energy Functional 

In general, we may consider a region of interest W in a 

Euclidean space R n . Let x designate the pixel position in 

W. Thus, for 3D spatial data, we have n = 3. Our results are 

based on the processing of a slice from a brain image, so n = 

2, and W is a two-dimensional (2D) region, and the vector 

x is a 2D position vector in, for instance, Cartesian coordinates. 

Over this region W, estimation of a field u = u(x) is 

of interest, and measurements g = g(x) are collected. The 

following energy functional [30] for scalar fields is based on 

the energy functional of References [31] and [32] 

Raw Tensor Data, g 

Specifications of: 

(1) Weights a, b, r 

(2) Data Fidelity Model, f 

(3) Data Continuity Model, h 

Variational Segmentation 

and Smoothing 

58 Model-Based Variational Smoothing and Segmentation for Diffusion Tensor Imaging in the Brain 

(1) 

Edge Data, v 

Smoothed Data, u 

We generalize the above functional to vector field smoothing 

(introduction of tensor notation at this stage, although 

more cumbersome, provides no additional insight) with the 

introduction of the data fidelity and continuity functions 

(h 1 (u), h 2 (g)), and f(u), respectively 

For a given data g and choices of functions h 1 (u), h 2 (g), and 

f(u), the energy functional is minimized with respect to u 

and v. Input data g and smoothed data u are vector fields 

(tensor processing can be recast as vector processing) of 

dimensions m and r, respectively, whereas v is a scalar field 

that represents the edges of the smoothed vector field u. 

Further g, u and v are continuous n-dimensional fields and 

are defined for all x in region W in an n dimensional space x. 

The first term in the above functional represents a smoothing 

penalty term that favors spatial smoothness of vector 

field f(u), rather than of u, at all interior points of the region, 

where edge field v

of edges. The constants a, b, and r represent the chosen 

weights on the accompanying cost components and determine 

the nominal smoothing radius, the edge width, as well 

as govern the value of edge function v. Specifically, the ratio 

a/b is related to the nominal smoothing radius, r to the 

edge width, and a governs the edge strength. Further details 

governing the choice of constants a, b, and r is discussed 

in Reference [33]. For more details on the segmentation 

approach and on the results of the application of the functional 

for smoothing and segmentation of phantom, MRI 

and functional magnetic resonance imaging (fMRI) scalar 

data, as well as for the fusion of different modality data, see 

References [33]-[36] and the references therein. 

The edges are estimated based on continuity attributes f(u) 

of the smoothed tensor field u and the specified prior model 

on edge field. The Euler Lagrange equations that are the 

necessary conditions associated with the minimization of 

the energy functional can be solved by the gradient descent 

method (e.g., References [33]-[35]). 

From the outputs u and v, additional relevant attributes 

associated with size, shape, and orientation of the diffusion 

ellipsoid may be distilled for further analysis. Example attributes 

include the trace (for diffusion magnitude), anisotropy 

measures (for diffusion “shape”), and the direction 

of eigenvectors (for diffusion orientation). [37] The ability 

to select functions f(u) and h1(u), h2(g) to satisfy various 

continuity and data fidelity requirements, respectively, is an 

important advantage that enables the viewing of the same 

DTI data from different perspectives. 

Application to DTI Data 

Depending on the objective, one can select the continuity 

functions h1(u), h2(g) and fidelity function f(u) to obtain 

an edge field v and an accompanying smoothed tensor 

field u with respect to specific features of the data. Differential 

smoothing concerns can thus be applied to different 

weighted eigenspace components of the tensor, and more 

generally, to any other sets of attributes of the tensor. 

We next illustrate two different models that capture different 

characteristics of spatial similarity for the tensor data 

by selection of different forms of continuity function f(u) 

and the data fidelity function h2 (g) while retaining the same 

form of function h1 (u) = u 

(a) Normalized tensor smoothing 

(b) Dominant directional tensor component smoothing 

where l1 is the maximum of the three eigenvalues of the 

tensor g. 

The first model represents a scale-invariant continuity criterion 

for the tensor data g. By contrast, the second model 

assumes the same invariance continuity criterion as the 

first, but with respect to only the subspace of tensor g associated 

with its dominant eigenvector s 1 . The objective of 

identifying regions of spatial continuity within the image, or 

equivalently, segmenting, motivates the choice of model. It 

may be noted that for dominant directional tensor smoothing 

in (b) above, we have chosen to work in the rank-1 

dominant tensor space s 1 s T 1 rather than the vector space of 

associated direction s 1 . 

For measures, we adopt the following choices for F, H of 

Eq. (2) 

Model-Based Variational Smoothing and Segmentation for Diffusion Tensor Imaging in the Brain 59 

(3) 

(4) 

where F and H represent the Euclidean norm of the gradient 

of f(u) and the estimated error u - h 2 (g), respectively. 

Assessment 

In order to assess the results of the application of this processing 

to clinically relevant DTI data, we selected a representative 

axial slice that included a comprehensive set of neuroanatomic 

white matter regions of interest (ROIs). These anatomic 

regions include the corpus callosum, internal capsule, 

superior longitudinal fasciculus, and cingulum bundle. 

First, we visually inspect the results of the smoothing 

modes on the appearance of fractional anisotropy (fa) maps 

as well as in visualization of tensor orientation information. 

Second, we quantify these observations by evaluating the 

distribution of fa values over the anatomic regions listed 

above. Third, we evaluate the sensitivity of the proposed 

methodology by comparing, using images and the change 

in performance with traditional methods when noise is 

added to the raw data. We choose to add Gaussian noise at 

increasing levels to the data, with negative values set to zero 

to remain within the physical constraint of non-negative 

intensity. In addition to comparing the proposed method 

and the traditional approach using images, we also quantify 

the effect of noise on the performance of the proposed 

approach in terms of the coefficient of variation of the fa 

over each anatomic region of interest. 

results 

In this section, we demonstrate the operation of the algorithm 

in the context of two different smoothing models, 

characterize this processing in the context of anatomic 

information contained within the DTI data, and summarize 

some of the noise properties of the implementation. Figure 

2 demonstrates a number of different views of the results 

of this smoothing procedure on an axial brain slice. This 

includes the raw (unsmoothed) data in the first column as 

well as the results of the two different smoothing models: 

normalized tensor in the second column, and directional 

projection in the third column. The “cuboid” and color 

representations [38] of the directional information contained

Edges, n 

Fractional 

Anisotropy, fa 

‘Cuboid’ 

Display 

Directional 

Color Coding 

Unsmoothed 

Smoothed 

Normalized 

Tensor 


Smoothed 

Directional 

Projection 

Figure 2. Effect of two smoothing models (2 nd and 3 rd columns) on an axial brain slice. The fractional anisotropy and edge 

maps are displayed in the first two rows, and the “cuboid” and color representations of the directional information 

contained in the resultant tensor fields are displayed in the last two rows. Maximum details emerge when smoothing 

is most selective, directional projection based (3 rd column), within the edge field boundaries.

in the resultant tensor fields are presented in the third and 

fourth rows, respectively. 

From the edge field visualization in the first row, it is clear 

that the most details consistent with the anatomic structure 

emerge when smoothing is most selective within the 

edge field boundaries. Specifically, the edge map in the 

third column, which is based on the directional projection, 

displays more details than the edge map in the second 

column, which is based on the normalized tensor. 

The second row of images indicates that the impact of 

edge preservation on the smoothing of the tensor field 

and its components can also be appreciated from the fa 

images for the smoothed tensor. The raw data’s fractional 

anisotropy is shown in the first column for comparison. 

It might be remarked that by definition, the fractional 

anisotropy of the directional component in the raw data 

will be unity and of interest is the deviation from unity that 

arises from the spatial variation of the dominant direction 

component that is reflected in the smoothing. The quantitative 

impact of different modes of smoothing is presented 

Table 1. 

in Table 1. This includes the mean and standard deviation 

of the functional anisotropy fa (as well as the coefficient of 

variation (CV)) for five anatomically motivated and manually 

defined regions annotated in Figure 3. These regions 

were identified by a trained neuroanatomist using both 

tensor orientation and anisotropy information. For the case 

of normalized tensor smoothing, SNR, or equivalently the 

reciprocal of the CV, is improved for all regions except for 

lateral ventricle whose edges with the adjacent region of the 

internal capsule are not well delineated, resulting in loss of 

restricted regional smoothing at the border of that region. For 

the case of directional smoothing, SNR values are uniformly 

enhanced for all regions due to better regional edge details 

and attendant region limited smoothing. The CV is reduced 

by at least 2.5-fold when comparing directional smoothing 

to the original measures of anisotropy, indicating a concomitant 

increase in the resultant SNR for these measures. 

The “cuboid” displays in the third row of Figure 2 can explain 

the superior performance of the directional projection method 

in the third column. These cuboid displays are better appreciated 

by looking at a closeup of particular regions, as is done in 

Raw Tensor fa Smoothed Smoothed Dominant 

Normalized Directional Tensor 

Tensor fa Component fa 

Corpus Callosum 

Mean (m) 0.646 0.5806 0.9575 

Std. Dev (s) 0.117 0.1014 0.0493 

CV (100 s/m) 18.1 17.46 5.14 

Cingulum Bundle 

Mean (m) 0.5524 0.4306 0.9238 

Std. Dev (s) 0.151 0.0953 0.0515 

CV (100 s/m) 27.3 22.13 5.57 

Internal Capsule 

Mean (m) 0.3615 0.28 0.9308 

Std. Dev (s) 0.0768 0.0493 0.0620 

CV (100 s/m) 21.24 17.61 6.67 

Superior Longitudinal 

Fasciculus 

Mean (m) 0.5676 0.4928 0.9496 

Std. Dev (s) 0.1078 0.0799 0.0598 

CV (100 s/m) 18.99 16.21 6.30 

Lateral Ventricle 

Mean (m) 0.2647 0.2078 0.8103 

Std. Dev (s) 0.1136 0.1233 0.0883 

CV (100 s/m) 42.92 59.34 10.90 

This table demonstrates the quantitative impact of different modes of smoothing and segmentation in 

terms of mean, standard deviation and coefficient of variation (CV) statistics of fractional anisotropy fa in 

five different regions of the brain for the particular 2-D slice of DTI data shown in Figure 4. The CVs are 

lowest, an indication that directional smoothing yields effective segmentation of homogeneous regions. 


CC Corpus Callosum 

IC Internal Capsule 

SLF Superior Longitudinal 

Fasciculus 

CG Cingulum Bundle 

lv Lateral Ventricle 

Figure 3. Manual delineation of five anatomically motivated 

regions for further analysis (Figure 6, Table 

1) of impact of different modes of smoothing 

and segmentation on fractional anisotropy of 

smoothed tensor in the regions. Delineations 

were based on tensor orientation and anisotropy 

and are shown with respect to the fractional 

anisotropy map here. 

the second row of Figure 4. The closeup region, a portion of 

the cerebral hemisphere, is indicated in the top image of the 

first row. We added images displaying the dominant direction 

vectors for the raw data, the smoothed normalized tensor, 

and the smoothed directional projection in the third row of 

Figure 4 for the sake of comparison. Again, we see that direction 

details are better kept using the smoothed directional 

projection. One example is the region above the thick arrows, 

where directional (curved corners) structure is preserved in 

the directional image, but smoothed over in the normalized 

tensor image. Comparison of other parts of the closeup views 

leads to a similar conclusion. It is this preservation of the higher 

dimensional directional characteristics of the tensor at the pixel 

level that is responsible for the superior image obtained from 

the directional projection method. 

We now consider added noise, our third assessment 

criterion. The effect of added noise is evaluated to 

establish the robustness of the approach. In Figures 5 

and 6, we compare the results of increasing noise levels 

added to the raw data. Levels of the additional noise 

range from 0 (no simulated noise added) to approximately 

5 times the estimated sigma value. The sigma 


value was estimated from the raw data outside the 

brain. These images include: top row – raw data fractional 

anisotropy (fa); second row – smoothed fractional 

anisotropy; third row – our edge field v; bottom 

row - conventional Sobel edge field of raw fa. Using 

anatomically-based ROIs, Figure 6 illustrates, for the 

corpus callosum region, that the smoothed tensorbased 

estimate of regional anisotropy fa in the second 

row of Figure 5 has a substantially lower coefficient of 

variation (bottom curve in Figure 6) than the original 

data (top curve in Figure 6); the reduction is by almost 

a factor of 10. Similar reductions were obtained for all 

other regions of Figure 4: cingulum bundle, superior 

longitudinal fasciculus, and internal capsule. Additionally, 

as Figure 5 indicates, comparison of edge fields 

from our approach on the third row with a conventional 

Sobel edge field on the fourth row illustrates that, while 

added noise has a deleterious effect on the Sobel edge 

field, the new models introduced to the energy functional 

preserve details even as noise is added. 

Discussion 

The above results demonstrate the model-based variational 

segmentation functional approach’s ability to provide a 

diverse collection of output images within a unified framework. 

The usefulness of the variational segmentation function 

approach has been demonstrated for other forms of 

brain imaging, such as structural [34] and functional magnetic 

resonance imaging data. [35] 

The versatility of these functionals, in their ability to 

produce a diverse collection of output images, is an important 

addition to the methods or tools available for image 

analysis. This innovation provides a unified framework 

for spatially selective smoothing of noisy brain image 

data along attributes of choice derived from the diffusion 

tensor whereby we can adaptively determine smoothed 

regions within the white matter that are relatively homogeneous 

with respect to specific tensor properties of 

shape, size, and orientation of the associated diffusion 

ellipsoid. In addition to providing a demarcation of the 

regions with respect to user-specified attributes of homogeneity 

in the DTI data, the segmentation functional is 

amenable and flexible to using prior information on attributes 

of both the tensor and edge field with incorporation 

of additional penalty terms in the functional. Determining 

smoothed regions with specific tensor properties 

enhances the ability to characterize the morphometric 

properties of the compact portion, or “stem,” of the major 

white matter pathways in regions where partial volume 

problems and the validity of the tensor assumption are 

less problematic. [14] 

A comparison has been presented of attributes such as 

anisotropy and direction of diffusion for the raw tensor 

itself without smoothing, the smoothed normalized tensor,

Fractional 

Anisotropy, fa 

‘Cuboid’ 

Display 

Dominant 

Direction 

Unsmoothed 

Smoothed 

Normalized 

Tensor 

Smoothed 

Directional 

Projection 

Figure 4. Closeup displays demonstrate the effect of normalized tensor (2 nd column) and directional projection (3 rd column) 

smoothing more clearly by displaying the ‘cuboid’ (2 nd row) and dominant direction vector (3 rd row) of the principal 

eigenvector for these two models for a portion of the cerebral hemisphere marked on fractional anisotropy display. 

Region above thick arrows are one example where directional projection preserves details more visibly. 


Raw or 

Original 

fa 

Smoothed 

fa 

Our 

Edge Field 

v 

Conventional 

Sobel 

Edge Field 

Sigma Level 

of Added 

Noise 

sobeledge sobeledge sobeledge sobeledge sobeledge sobeledge 

0 1 2 3 4 5 

Original 

Data 

Increasing Noise Level 

Figure 5. Effect of added noise on raw fa, smoothed fa, our edge field v, and conventional Sobel edge field. 

The directional projection-based smoothing and segmentation (2 nd and 3 rd) row are more robust to 

added noise. 

Coefficient of Variation 

Corpus Callosum 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

fa-sm fa-sm fa-sm fa-sm fa-sm fa-sm 

edge-sm edge-sm edge-sm edge-sm edge-sm edge-sm 

Original 

Data 

Original 

Smoothed 

0 1 2 3 4 5 

Sigma level of Added Noise 


Figure 6. Effect of noise on smoothing. The 

coefficient of variation of the smoothed fa 

(bottom curve) corresponding to the second 

row of images in Figure 5 is significantly 

lower than that of the raw or original fa 

(top curve) corresponding to the first row 

of Figure 5. Curves are for corpus callosum 

region. Similar results obtain for other 

regions in Figure 3.

and the smoothed tensor component associated with the 

dominant eigenvector. The underlying diffusion characteristics 

of the white matter in the brain motivate the choice 

of these mappings, whereas normalization provides scale 

invariance of salient features. Therefore, it is possible to 

visualize attributes of anisotropy and direction of the resultant 

tensor fields and the associated edge field in various 

ways. In this fashion, the applicability of a unified and 

versatile image processing framework for smoothing and 

feature extraction in support of fiber pathway identification 

within the human brain is demonstrated. 

Specifically, promise of the utility of the variational simultaneous 

smoothing and segmentation functional to improve 

the characteristics of tensor-valued imaging data has been 

demonstrated. The result is an improvement of the overall 

signal that preserves the anatomic detail. Within the 

directional component smoothing case, regions of discrete 

directionality are smoothed, but transitions between 

regions are well preserved. This can be particularly well 

seen as one traverses from the cortex toward the central 

portion of the images shown in Figure 4. The white matter 

contained within the gyral folds near the cortex remains 

nicely visualized and oriented “out” of the gyri. Transitions 

of radially oriented white matter of the corona ratiata and 

U fibers with the perpendicularly oriented internal capsule 

and various associational pathways are clearly demarked. 

This level of detail is only retained in the directional 

smoothing case. Finally, it should be noted that visualization 

based on the dominant direction coding in Figure 2 is 

less sensitive to the underlying variations and noise structure, 

presumably due to the subtleties of the variations in 

intensity of directional noise compared to the large color 

differences of the different fiber systems. For the images 

examined, directional smoothing thus seems appropriate 

because of the simple fact that it simultaneously smooths 

while preserving directionality. This smoothing can act as 

a preprocessing step for virtually any subsequent processing 

of the diffusion data, such as between group analyses 

of anisotropy data, [11],[39] anatomic regional characterization, 

[40] and tractographic reconstruction. [41]-[43] 

Turning to the results of Figures 5 and 6, we examine 

respectively two aspects: the edges and the coefficient of 

variation over ROIs. First, as the graph demonstrates, the 

coefficient of variation of fa calculated over the anatomic 

region of the corpus callosum is dramatically reduced 

(improved) with simultaneous smoothing and segmentation, 

and that this substantial improvement holds even in 

the presence of the greatly reduced image quality at the 

maximum added noise. 

Turning to the edges in Figure 5, we observe that with 

incrementally increasing noise added to the raw data, 

the conventional (Sobel) edge field is seen to deteriorate 

more rapidly. By contrast, with our approach, edges are 

maintained at the increased noise levels. This result is a 

direct consequence of working with a most dominant 

feature of the tensor, specifically, the dominant rank-1 

tensor. 

Limitations 

A method that is generalizable in terms of processing image 

data and its dimensionality is presented. The application 

used to illustrate the processing, namely DTI, is an important 

and new radiological tool for the clinical assessment of 

cerebral white matter. Processing can improve the resultant 

SNR without penalizing the resultant spatial resolution, and 

thus can enhance the utility of these measurements. This 

improvement in SNR can be used to shorten the potentially 

lengthy diffusion acquisition time. It is acknowledged that 

the tensor acquisition may not be optimal for observation 

of specific fiber tracts themselves, and that this acquisition 

optimization is an open research question. These 

processing tools, however, will extend to a higher order 

(i.e., q-space and high angular resolution) diffusion acquisitions, 

[44]-[46] and can still play an important role in the 

processing and analysis of these classes of data acquisition. 

Indeed, the utility of submodel-based smoothing becomes 

even more important as the complexity of the input data 

increases. The flexibility of the methods we report here can 

be adapted easily for processing models defined in terms 

of any matrix decomposition of the acquired data, not just 

the eigen-decomposition typical in the six-direction tensor 

acquisitions. Also, there is a spatial resolution tradeoff 

between the need for high resolution to observe subtle white 

matter pathways and the acquisition time available for the 

subjects. These processing tools will be helpful to extend 

the limits of SNR in the extraction of meaningful anatomic 

information. An additional area of potential impact for a 

tool such as this includes utilizing tensor information in 

solving for neural systems-based functional imaging. [47]- 

[49] It might be remarked that the focus of the reported 

work is the model-based optimal extraction of information 

for a given SNR and DTI data acquisition parameters, and 

future work remains necessary for optimization involving 

SNR and data acquisition parameters. 

We note that the simultaneous smoothing and segmentation 

process can change the nature of the error in the 

smoothed estimates and the use of smoothed estimates for 

further analysis, such as for group analysis, which may need 

to employ alternate analysis approaches that are not necessarily 

based on a specific noise model assumption such as 

Gaussian noise. For example, for decision support, methods 

such as support vector machines can be employed. 

In addition, the method’s appeal is the flexibility to use 

various lower dimensional attributes of the higher dimensional 

data using functions F and H, and we demonstrate 

this strength here primarily in the context of 2D data. The 

method, however, can be readily applied to 3D data. In the 


case of 3D analysis, additional terms associated with gradients 

of the data and edge fields in the added third dimension 

arise in the energy functional E of (2). We, therefore, have 

edge surfaces in 3D that are smoother than those obtainable 

from edge boundaries produced by the 2D analysis. 

To conclude, we have presented a general framework for 

smoothing diffusion tensor data and have developed a tool 

to execute this processing. The preferred choice of the fidelity 

and continuity functions h1 (u), h2 (g) and f(u) generally 

will depend on both the image and the objective of the 

image analysis task. There is no universal image model that 

outperforms all others in all situations. Moreover, different 

regions of the data domain require segmentations based 

on more than one model. An important objective in this 

study is, therefore, to identify for DTI data a small number 

of potent models that can be adapted for effective segmentation. 

Further, as no single model applies over the entire 

image due to variations in the underlying tissue and partial 

volume effects, adaptive learning of relevant features at 

every voxel based on neighborhood characteristics is another 

focus of ongoing research. The improved output data will 

enable a more refined analysis, including segmentation of 

white matter substructures using various manual and automated 

techniques. 

acknowledgment 

This work supported by PHS Research Grant no. 2 R01 

NS34189 from the National Institute of Neurological Disorders 

and Stroke (NINDS), National Cancer Institute (NCI) 

and National Institute of Mental Health (NIMH), as part of 

the Human Brain Project, and a Draper Laboratory R&D 

project. We also acknowledge Van Wedeen and David Tuch 

for helpful discussions and visualization tools. 

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68 Model-Based Variational Smoothing and Segmentation for Diffusion Tensor Imaging in the Brain

(l-r) Mukund N. Desai and 

Rami S. Mangoubi 

bios 

Mukund Desai is a Distinguished Member of the Technical Staff at 

Draper Laboratory. He has led research in optimal control, planning, 

estimation, optimal and robust detection, and image processing. 

His research work found novel applications at Draper in aircraft 

flight path management, path planning, battlefield management, 

mine hunting, target tracking, and distributed sensing. He holds 

two patents for helicopter swash-plate control and for finite capacity 

interaction processes. He has three more patents under filing. He 

has numerous technical publications, including two book chapters. 

Current research activities include the development of robust non- 

Gaussian and nonlinear signal modeling, learning, and detection, 

with application to chemical sensing, image and signal processing. His current work in multidimensional estimation has been 

applied to simultaneous denoising and segmentation of structural, functional magnetic resonance images and diffusion tensor 

images. He is also interested in ad hoc communication between distributed sensors, with application to the detection of transient 

phenomena. He also supervises graduate students conducting their research at Draper. He received BS and MS degrees 

with distinction from the Indian Institute of Science (IISc), Bangalore, India, and a PhD in Applied Mathematics from Harvard 

University. 

David N. Kennedy is an Associate Professor of Neurology at the Harvard Medical School, and jointly appointed in the Neurology 

and Radiology Departments at the MGH. He has extensive expertise in the development of image analysis techniques 

and co-founded the Center for Morphometric Analysis at MGH. He has participated in the advent of such technologies as 

MRI-based morphometric analysis (1989), functional MRI (1991), and diffusion tensor pathway analysis (1998). He has longstanding 

experience with the development of neuroinformatics resources (Internet Brain Volumetric Database, Internet Brain 

Segmentation Repository, Internet Analysis Tools Registry), is co-Principal Investigator of the morphometry Biomedical Informatics 

Research Network (mBIRN), has been a Human Brain Project grant recipient since 1996, and is a founding editor of 

Neuroinformatics, which debuted in 2003. 

Rami Mangoubi is a Senior Member of the Technical Staff at Draper Laboratory. He has worked on problems and led projects 

in operations research, control, alignment and calibration, and statistical signal detection, with a wide range of applications 

including computer networks, control of and failure detection in autonomous and space vehicles, biochemical sensing, 

magnetic resonance brain imaging and components mathematical model development and validation. Earlier in his career, he 

introduced the use of robust game theoretic filters for failure detection in dynamic plants. Current research includes robust non- 

Gaussian signal detection and cellular imaging. His numerous publications include Robust Estimation and Failure Detection: A 

Concise Treatment (Springer Verlag, London, UK, 1998). He supervises graduate students conducting their research at Draper. 

Dr. Mangoubi was an invited plenary speaker for the 2000 International Federation of Automatic Control’s (IFAC) SAFEPRO- 

CESS conference in Budapest, Hungary. He is currently a principal investigator on an NIH research grant in the area of cellular 

imaging. He is a member of the IFAC SAFEPROCESS Technical Committee and a senior member of AIAA. He received a BS in 

Mechanical Engineering, an MS in Operations Research, and a PhD in Detection, Estimation, and Control from MIT. 


70 2006 Published Papers 

published 

2006 

Papers 

Aceti, J.; Bernstein, J.; Borenstein, J.T.; Clark, H.A.; 

Zapata, A.M. 

Engineering Solutions to Problems of National 

Significance: Applying Biomedical Engineering Technologies 

to Healthcare Needs 

Explorations, The Charles Stark Draper Laboratory, Inc., 

Fall 2006 

Abramson, M.R.; Carter, D.W.; Collins, B.K.; 

Kolitz, S.E.; Miller, J.V.; Scheidler, P.J.; Strauss, C.M. 

Operational Use of EPOS to Increase the Science 

Value of EO-1 Observation Data 

6 th Earth Science Technology Conference (ESTC), Baltimore, 

MD, June 26-29, 2006. Sponsored by: NASA’s 

Earth-Sun Systems Technology Office (ESTO) 

Armstrong, J.T.; Mozurkewich, D.; Hajian, A.R.; 

Johnston, K.J.; Thessin, R.N.; Peterson, D.M.; 

Hummel, C.A.; Gilbreath, G.C. 

The Hyades Binary Theta Squared Tauri: Confronting 

Evolutionary Models with Optical Interferometry 

Astronomical Journal, Vol. 131, No. 5, May 2006 

Benson, D.A.; Rao, A.V.; Huntington, G.T.; 

Thorvaldsen, T. P. 

Direct Trajectory Optimization and Costate Estimation 

via a Gauss Pseudospectral Method 

AIAA Guidance, Navigation, and Control Conference, 

Keystone, CO, August 21-24, 2006 

Bernstein, J.J.; Lee, T.W.; Rogomentich, F.J.; 

Bancu, M.G.; Kim, K.H.; Maguluri, G.; Bouma, 

B.E.; DeBoer, J.F. 

Magnetic Two-Axis Micromirror for 3D OCT 

Endoscopy 

2006 Solid State Sensors, Actuators, and Microsystems 

Workshop, Hilton Head, SC, June 4-8, 2006, pp. 7-10 

Bettinger, C.J.; Orrick, B.; Misra, A.; Langer, R.; 

Borenstein, J.T. 

Microfabrication of Poly (Glycerol-Sebacate) for 

Contact Guidance Applications 

Biomaterials, Elsevier, Vol. 27, No. 12, April 2006, pp. 

2558-2565 

Bettinger, C.J.; Weinberg, E.J.; Kulig, K.M.; 

Vacanti, J.P.; Wang, Y.; Borenstein, J.T.; Langer, R. 

Three-Dimensional Microfluidic Tissue-Engineering 

Scaffolds Using a Flexible Biodegradable Polymer 

Advanced Materials, Vol. 18, No. 2, January 19, 2006, 

pp. 165-169 

Bickford, J.A. 

Extraction of Antiparticles Concentrated in Planetary 

Magnetic Fields. Phase I Study 

NASA Institute for Advanced Concepts (NIAC) Fellows 

Meeting, March 8, 2006, Atlanta, GA 

Bickford, J.; Schmitt, W.M.; Spjeldvik, W.N.; 

Gusev, A.; Pugacheva, G.I.; Martin, I. 

Natural Sources of Antiparticles in the Solar System 

and the Feasibility of Extraction for High Delta-V 

Space Propulsion 

New Trends in Astrodynamics and Applications, III, 

Princeton, NJ, August 16-18, 2006. Sponsored by: 

American Institute of Physics (AIP) 

Borenstein, J.T. 

The Role of Engineering in Advancing Health Care 

in the 21 st Century 

Presentation posted on Wentworth Institute of Technology’s 

web site 

Candler, R.N.; Duwel, A.; Varghese, M.; 

Chandorkar, S.; Hopcroft, M.; Park, W.T.; Kim, B.; 

Yama, G.; Partridge, A.; Lutz, M.; Kenny, T.W. 

Impact of Geometry on Thermoelastic Dissipation in 

Micromechanical Resonant Beams 

IEEE JMEMS, Vol. 15, No. 927, 2006 

Carlen, E.T.; Weinberg, M.S.; Dube, C.E; 

Zapata, A.M.; Borenstein, J.T. 

Micromachined Silicon Plates for Sensing Molecular 

Interactions 

Applied Physics Letters, AIP, Vol. 89, No. 17, October 

23, 2006

Cernosek, R.W.; Robinson, A.L.; Cruz, D.Y; 

Adkins, D.R.; Barnett, J.L.; Bauer, J.M.; Blain, M.G.; 

Byrnes, J.E.; Dirk, S.M.; Dulleck, G.R.; Ellison, J.A.; 

Fleming, J.G.; Hamilton, T.W.; Heller, E.J.; 

Howell, S.W.; Kottenstette, R.J.; Lewis, P.R.; 

Manginell, R.P.; Moorman, M.W.; Mowry, C.D.; 

Manley, R.G.; Okandan, M.; Rahimian, K.; 

Shelmidine, G.J.; Shul, R.J.; Simonson, R.J.; 

Sokolowski, S.S.; Spates, J.J.; Staton, A.W.; 

Trudell, D.E.; Wheeler, D.R.; Yelton, W.G.; Eds.: 

Thomas, G.; Zhong-Yang, C. 

Micro-Analytical Systems for National Security 

Applications 

Micro (MEMS) and Nanotechnologies for Space Applications, 

April 19-20, 2006, Kissimmee, Florida 

Chen, D.; Lin, P.J. 

Minimum Energy Path Planning for Ad Hoc 

Networks 

Wireless Communications and Networking Conference 

(WCNC), Las Vegas, NV, April 3-6, 2006. Sponsored by: 

IEEE 

Davis, C.E.; Krebs, M.D.; Tingley, R.D.; 

Zeskind, J.E.; Holmboe, M.E.; Kang, J.-M. 

Alignment of Gas Chromatography-Mass Spectrometry 

Data by Landmark Selection from Complex 

Chemical Mixtures 

Chemometrics and Intelligent Laboratory Systems, Vol. 

81, No.1, March 2006, pp. 74-81 

Desai, M.N.; Kennedy, D.N.; Mangoubi, R.S.; 

Shah, J.; Karl, C.; Worth, A.; Makris, N.; Pien, H. 

Model-Based Variational Smoothing and Segmentation 

for Diffusion Tensor Imaging in the Brain 

Neuroinformatics, Vol. 4, No. 3, 2006, pp. 217-234 

Desai, M.N.; Mangoubi, R.S.; Kennedy, D. 

Robust Constrained Non-Gaussian fMRI Detection 

International Symposium on Biomedical Imaging from 

Nano to Macro, Arlington, VA, April 6-9, 2006. Sponsored 

by: IEEE 

Dever, C.; Mettler, B.; Feron, E.; Popovic, J.; 

McConley, M. 

Nonlinear Trajectory Generation for Autonomous 

Vehicles Via Parameterized Maneuver Classes 

Journal of Guidance Control and Dynamics, Vol. 29, No. 

2, March-April 2006, pp. 289-302 

Duwel, A.E.; Candler, R.N.; Kenny, T.W.; 

Varghese, M. 

Engineering MEMS Resonators with Low Thermoelastic 

Damping 

Journal of Microelectromechanical Systems, IEEE, Vol. 

15, No. 6, December 2006, pp. 1437-1445 

Fucetola, C.; Carter, D.J. 

Process Latitude of Deep-Ultraviolet Conformable 

Contact Photolithography 

50 th International Conference on Electron, Ion, and 

Photon Beam Technology and Nanofabrication, Baltimore, 

MD, May 30-June 2, 2006 

Fuhrman, L.R. 

Future of Lunar Landing Systems 

29 th Rocky Mountain Guidance and Control Conference, 

Breckenridge, CO, February 4-8, 2006, Advances 

in the Astronautical Sciences, Vol. 125, 2006, pp. 

213-223. Sponsored by: American Astronautical Society 

(AAS) 

Gustafson, D.E.; Elwell Jr., J.M.; Soltz, J.A. 

Innovative Indoor Geolocation Using RF Multipath 

Diversity 

Position Location and Navigation Symposium (PLANS), 

San Diego, CA, April 25-27, 2006. Sponsored by 

IEEE/ION 

Harjes, D.I.; Clark, H.A. 

Novel Optical Biosensor Arrays for Toxicity Screening 

in Drug Discovery 

57 th Pittsburgh Conference on Analytical Chemistry and 

Applied Spectroscopy (PITTCON), Orlando, FL, March 

12-17, 2006 

Hattis, P.D.; Campbell, D.P.; Carter, D.W.; 

McConley, M.; Tavan, S. 

Providing Means for Precision Airdrop Delivery from 

High Altitude 

AIAA Guidance, Navigation, and Control Conference, 

Keystone, CO, August 21-24, 2006 

Hawkins, A.M.; Fill, T.J.; Proulx, R.J.; Feron, E.M.J. 

Constrained Trajectory Optimization for Lunar 

Landing 

Spaceflight Mechanics 2006, Tampa, FL, January 22-26, 

2006, Advances in the Astronautical Sciences, Part I, Vol. 

124, 2006, pp. 815-836 

Heinrich, N.; Case, A.; Stein, R.L.; Clark, H.A. 

Optical Sensors for the Monitoring of Enzymatic 

Reaction for Drug Screening in Neurodegenerative 

Disease 

57 th Pittsburgh Conference on Analytical Chemistry and 

Applied Spectroscopy (PITTCON), Orlando, FL, March 

12-17, 2006 

Hildebrant, R. 

Framework for Autonomy 

Optics East, International Symposium, Boston, MA, 

October 1-4, 2006. Sponsored by: SPIE 

2006 Published Papers 71


Hopkins III, R.E. 

MEMS Inertial Technology. A Short Course 

PLANS, San Diego, CA, April 25-27, 2006. Sponsored 

by: IEEE/ION; Joint Navigation Conference (JNC), Las 

Vegas, NV, May 1-4, 2006. Sponsored by: Joint Service 

Data Exchange (JSDE) 

Huntington, G.T.; Rao, A.V. 

Optimal Reconfiguration of a Tetrahedral Formation 

Via a Gauss Pseudospectral Method 

Advances in the Astronautical Sciences, AAS, Vol. 123, 

Part II, 2006, pp. 1337-1358 

Huntington, G.T.; Benson, D.A.; Rao, A.V. 

Post-Optimality Evaluation and Analysis of a Formation 

Flying Problem Via a Gauss Pseudospectral 

Method 

Advances in the Astronautical Sciences - Proceedings of 

the AAS/AIAA Astrodynamics Conference, Vol. 123, No. 

2, 2006 

Jang, J-W.; Fitz-Coy, N.G. 

Differential Games: A Pole Placement Approach 

Proceedings of the University at Buffalo, State University 

of New York/AAS Malcolm D. Shuster Astronautics 

Symposium, Grand Island, NY, Vol. 122, 2006 

Johnson, M.C. 

Parameterized Approach to the Design of Lunar 

Lander Attitude Controllers 

Guidance, Navigation, and Control Conference, 

Keystone, CO, August 21-24, 2006. Sponsored by: 

AIAA 

Keegan, M.E.; Saltzman, W.M. 

Surface-Modified Biodegradable Microspheres for 

DNA Vaccine Delivery 

Methods in Molecular Medicine, Vol. 127; DNA 

Vaccines: Methods and Protocols, 2 nd ed., Humana Press, 

2006 

Key, R.; Kahn, A.C., Deutsch, O.L. 

Midcourse Phase Inventory Management with 

Uncertain Threats 

Missile Defense Conference & Exhibit, Washington, DC, 

March 20-24, 2006. Sponsored by: AIAA 

Khademhossini, A.; Bettinger, C.J.; Karp, J.M.; 

Yeh, J.; Ling, Y.; Borenstein, J.T.; Fukuda, J.; 

Langer, R. 

Interplay of Biomaterials and Micro-scale Technologies 

for Advancing Biomedical Applications 

Journal of Biomaterials Science, Polymer Edition, Vol. 

17, No. 11, November 2006 

Khademhossini, A.; Langer, R.; Borenstein, J.T.; 

Vacanti, J.P. 

Microscale Technologies for Tissue Engineering and 

Biology 

Proceedings of the National Academy of Sciences of the 

USA, Vol. 103, No. 8, February 2006 

Kondoleon, C.A.; Marinis, T.F. 

Package Design for a Miniaturized Capacitive-Based 

Chemical Sensor 

39 th International Symposium on Microelectronics, San 

Diego, CA, October 8-12, 2006. Sponsored by: International 

Microelectronics and Packaging Society (IMAPS) 

Kourepenis, A.S.; Barbour, N.M.; Hopkins III, R.E.; 

Serna, F.J.; Varghese, M. 

MEMS Technologies and Applications 

International Test and Evaluation Association (ITEA) 

Annual Technology Review Conference, Cambridge, 

MA, August 8-10, 2006. Sponsored by: ITEA 

Krebs, M.D.; Mansfield, B.; Yip, P.; Cohen, S.; 

Sonenshein, A.L.; Hitt, B.A..; Davis, C.E. 

Novel Technology for Rapid Species-Specific 

Detection of Bacillus Spores 

Biomolecular Engineering, Vol. 23, February 2006, pp. 

119-127 

Krebs, M.D.; Kang, J.J.; Cohen, S.; Lozow, J.B.; 

Tingley, R.D.; Davis, C.E. 

Two-Dimensional Alignment of Differential Mobility 

Spectrometer Data 

Sensors and Actuators B (Chemical), Vol. 119, No. 2, 

December 2006, pp. 475-482 

Landis, D.L.; Thorvaldsen, T.P.; Fink, B.J.; 

Sherman, P.G.; Holmes, S.M. 

Deep Integration Estimator for Urban Ground 

Navigation 

PLANS, San Diego, CA, April 25-27, 2006. Sponsored 

by: IEEE/ION 

Lento, C.; McCarragher, B.; Magee, R. 

The CERAS Pod Test Cell for Simultaneous Environment 

Testing 

AIAA Missile Sciences Conference, Monterey, CA, 

November 14-16, 2006 

Lim, S.Y.; Miotto, P. 

Actuator Allocation Algorithm Using Interior Linear 

Programming 



AIAA

Lim, S.Y. 

Complementary Roll/Yaw Attitude Controller for 

Three-Axis Authority Momentum Spacecraft 



AIAA 

Lymar, D.S.; Neugebauer, T.C.; Perreault, D.J. 

Coupled-Magnetic Filters with Adaptive Inductance 

Cancellation 

IEEE Transactions on Power Electronics, Vol. 21, No. 6, 

November 2006, pp. 1529-1540 

Marinis, T.F.; Soucy, J.W.; Hanson, D.S.; 

Pryputniewicz, R.J.; Marinis, R.T.; Klempner, A.R. 

Isolation of MEMS Devices from Package Stresses by 

Use of Compliant Metal Interposers 

56 th Electronic Components and Technology Conference 

(ECTC), San Diego, CA, May 30-June 2, 2006. 

Sponsored by: IEEE, Components, Packaging, and 

Manufacturing Technology (CPMT) Society 

Masterson, R.A.; Miller, D. 

Dynamic Tailoring and Tuning of Structurally- 

Connected TPF Interferometer 

Proceedings of the SPIE, Vol. 6271, July 2006 

Masterson, R.A.; Miller, D. 

Hardware Tuning for Dynamic Performance Through 

Isoperformance Updating 

47 th Structures, Structural Dynamics, and Materials 

Conference, Newport, RI, May 1-4, 2006. Sponsored 

by: AIAA, ASME, American Society of Computer Engineers 

(ASCE), American Helicopter Society (AHS), ASC 

Mather, R.A.; Matlis, J. 

Alternative Approach to Testing Embedded Real- 

Time Software 

America’s Virtual Product Development (VPD) Conference: 

Evolution to Enterprise Simulation, Huntington 

Beach, CA, July 17-19, 2006. Sponsored by: MSC 

Software 

McAlpine, J.; Najjar, R.C.; Thompson, J. 

Hazmat Response: Victim Extrication, Trauma 

Control, and Decontamination in a Laboratory 

Setting 

Proceedings of the 24 th College and University Hazardous 

Waste Conference, August 6-9, 2006 

McCarragher, B.; Chen, B.; Chamberlin, S.; 

Magee, R. 

The Simultaneous Application of Vibration, Shock, 

and Thermal Missile Environments 

AIAA Missile Sciences Conference, Monterey, CA, 

November 14-16, 2006 

Mettler, B.; Feron, E.; Popovic, J.; McConley, M. 

Nonlinear Trajectory Generation for Autonomous 

Vehicles via Parameterized Maneuver Classes 

Journal of Guidance Control and Dynamics, AIAA, Vol. 

29, No. 2, March-April, 2006 

Miller, J.W.; Lommel, P.H. 

Biomimetic Sensory Abstraction Using Hierarchical 

Quilted Self-Organizing Maps 

Intelligent Robots and Computer Vision XXIV: Algorithms, 

Techniques, and Active Vision, Boston, MA, 

October 1-4, 2006. Sponsored by: SPIE 

Mitchell, I.T.; Gorton, T.B.; Taskov, K.; 

Drews, M.E.; Luckey, D.; Osborne, M.L.; 

Page, L.A.; Norris, H.L., III; Shepperd, S.W. 

GN&C Development of the XSS-11 Micro- 

Satellite for Autonomous Rendezvous and Proximity 

Operations 

29 th Guidance and Control Conference, Breckenridge, 

CO, February 4-8, 2006. Sponsored by: AAS 

Neugebauer, T.C.; Perreault, D.J. 

Parasitic Capacitance Cancellation in Filter 

Inductors 

Transactions on Power Electronics, IEEE, Vol. 21, No. 1, 

January 2006 

Pahlavan, K.; Akgul, F.O.; Heidari, M.; 

Hatami, A.; Elwell, J.M.; Tingley, R.D. 

Indoor Geolocation in the Absence of Direct Path 

IEEE Wireless Communications, Vol. 13, No. 6, December 

2006, pp. 50-58 

Perry, H.C.; Brady, T.M.; Breton, R.S.; Brodeur, S.J.; 

Brown, R.A.; Buckley, S.; Erikson, E.R.; 

Fuhrman, L.R.; Jackson, T.R.; Kochocki, J.A.; 

Turney, D.J.; Wyman Jr, W.F. 

Engineering Solutions to Problems of National 

Significance. Embedded Software and Draper IDEAS 

Explorations, The Charles Stark Draper Laboratory, Inc., 

Spring 2006 

Pierquet, B.J.; Neugebauer, T.C.; Perreault, D.J. 

Inductance Compensation of Multiple Capacitors 

with Application to Common- and Differential-Mode 

Filters 

IEEE Transactions on Power Electronics, Vol. 21, No. 6, 

November 2006, pp. 1815-1824 

Putnam, Z.R.; Braun, R.D.; Bairstow, S.H.; 

Barton, G.H. 

Improving Lunar Return Entry Footprints Using 

Enhanced Skip Trajectory Guidance 

Space 2006 Conference, San Jose, CA, September 19- 

21, 2006. Sponsored by: AIAA 

2006 Published Papers 73


Ricard, M.J.; Nervegna, M.F. 

Risk-Aware Mixed-Initiative Dynamic Replanning 

(RMDR) Program Update 

Unmanned Systems North America, Orlando, FL, 

August 29-31, 2006. Sponsored by: Association for 

Unmanned Vehicle Systems International (AUVSI) 

Roth, K.W.; Llana P.; Westphalen D.; Quartararo, L.; 

Feng M.Y. 

Advanced Controls for Commercial Buildings: 

Barriers and Energy Savings Potential 

Energy Engineering, 2006, Vol. 103, No. 6, pp. 6-36 

Rzepniewski, A.K.; Andrews, G.L. 

Legged Robot Motion with Explicit Stability 

Constraints: Theory and Application 

Unmanned Systems North America, Orlando, FL, 

August 29-31, 2006. Sponsored by: AUVSI 

Sawyer, W.D.; Prince, M.S 

Silicon on Insulator Inertial MEMS Device 

Processing 

MOEMS-MEMS Micro & Nanofabrication, Photonics 

West, San Jose, CA, January 21-26, 2006. Sponsored 

by: SPIE 

Schmidt, G.T. 

Future Navigation Systems: INS/GPS Technology 

Trends 

The Charles Stark Draper Laboratory, Inc., 2006 

Schmitt, W.M.; Larsen, D.E.; Brown, D.N.; 

Harris, Bernard S.; Zuckerman, H.L. 

Importance of Secondary Scattering in X-Ray 

Transport for Shadowing Analysis 

Hardened Electronics and Radiation Technology 

(HEART) Conference, Santa Clara, CA, March 6-10, 

2006. Sponsored by: Department of Defense (DoD)/ 

Department of Energy (DoE). 

Serklaud, D.K.; Peake, G.M.; Geib, K.M.; Lutwak, R.; 

Garvey, R.M.; Varghese, M.; Mescher, M. 

VCSELs for Atomic Clocks 

Vertical-Cavity Surface-Emitting Lasers X, Proceedings of 

SPIE, January 25-26, 2006, San Jose, CA 

Springmann, P.; Proulx, R.; Fill, T. 

Lunar Descent Using Sequential Engine Shutdown 

AIAA/AAS Astrodynamics Specialist Conference and 

Exhibit, Keystone, CO, August 21-24, 2006 

Stoner, R.; Walsworth, R. 

Atomic Physics - Collisions Give Sense of Direction 

Nature Physics, Vol. 2 , No. 1, January 2006, pp. 17-18 

Stubbs, A.; Vladimerou, V.; Fulford, A.T.; King, D.; 

Strick, J.; Dullerud, G.E 

Multivehicle Systems Control over Networks 

IEEE Control Systems, Vol. 26, No. 3, 2006, pp 56-69 

Tawney, J.; Hakimi, F.; Willig, R.L.; Alonzo, J.; 

Bise, R.T.; DiMarcello, F.; Monberg, E.M.; 

Stockert, T.; Trevor, D.J. 

Photonic Crystal Fiber IFOGs 

18 th International Conference on Optical Fiber Sensors, 

Cancun, Mexico, October 23-27, 2006. Sponsored by: 

Optical Society of America (OSA) 

Tetewsky, A.; Dow, B.; Bogner, T.; Mitchell, M.; 

Daley, S.; Shearer, J. 

Evaluating HYGPSIM’s New GPS/INS HWIL Prediction 

Capabilities with 2004 Reentry Vehicle Flight 

Data 

AIAA Missile Science Conference (Classified) Monterey, 

CA, November 14-16, 2006 

Weinberg, E.J.; Kaazempur-Mofrad, M.R. 

Large-Strain Finite-Element Formulation for Biological 

Tissues with Application to Mitral Valve Leaflet 

Tissue Mechanics 

Journal of Biomechanics, Vol. 39, No. 8, 2006, pp. 

1557-1561 

Weinberg, M.S.; Kourepenis, A.S. 

Error Sources in In-Plane Silicon Tuning-Fork MEMS 

Gyroscopes 

IEEE Journal of Microelectromechanical Systems, Vol. 

15, No. 3, June 2006, pp. 479-491 

Weinberg, M.S.; Wall, C.; Robertsson, J.; 

O’Neil, E.W.; Sienko, K.; Fields, R.P. 

Tilt Determination in MEMS Inertial Vestibular 

Prosthesis 

Journal of Biomechanical Engineering, Transactions 

of the ASME, Vol. 128, No. 6, December 2006, pp. 

943-56. 

Weinberg, M.S. 

Tuning Fork MEMS Gyroscopes 

Presented at Tufts University, October 12, 2006

Patents 

Introduction 

Draper Laboratory is well known for integrating 

widely diverse technical capabilities and 

technologies into innovative and creative 

solutions for problems of national importance. 

Draper’s scientists and engineers are actively 

encouraged to advance the application of science and 

technology, to expand the functions of existing technologies, 

and to create new ones. 

Draper has an established patent policy and understands 

the value of patents in directing attention to individual 

accomplishments. Disclosing inventions is an important 

step in documenting these creative efforts and is required 

under Laboratory contracts and by an agreement with 

Draper that all employees sign. Pursuing patent protection 

enables the Laboratory to pursue its strategic mission 

and to recognize its employees’ valuable contributions to 

advancing the state-of-the-art in their technical areas. An 

issued patent is also recognition by a critical third party 

(the U.S. Patent Office) of innovative work for which the 

inventor should be justly proud. 

Through December 31, 2006, 1297 Draper patent 

disclosures have been submitted to the Patent Committee 

since 1973; 655 of those were approved by Draper’s 

Patent Committee for further patent action. As of 

December 31, a total of 4804 patents have been granted 

for inventions made by Draper personnel. Twelve patents 

were issued for calendar year 2006. 

This year’s competition for Best Patent resulted in a tie. 

The featured patents are: 

Multi-gimbaled borehole navigation system 

and 

Flexural plate wave sensor 

The following pages present an overview of the technology 

covered in each patent and the official patent 

abstracts issued by the U.S. Patent Office. 

Patents Introduction 75

Multi-Gimbaled Borehole 

Navigation System 

Patent # 7,093,370 B2 Date Issued: August 22, 2006 

Mitchell L. Hansberry, Michael E. Ash, Richard T. Martorana 

76 Multi-Gimbaled Borehole Navigation System 

This invention addresses the need to monitor and guide the direction 

of a drill bit so that a borehole is created where desired. To determine 

the location of a drill bit in a borehole, the position and attitude must 

be known, including the vertical orientation and the north direction. 

Typically, gyroscopes can be used to determine the north direction, and accelerometers 

can be used to determine the vertical orientation. Prior systems have 

used single-orientation gyroscopes and/or single orientation accelerometers due 

to size limitations. However, these systems can suffer from long-term bias stability 

problems. 

Many prior systems attempted to determine the drill bit’s location accurately 

and efficiently, but each system had limitations. For example, where the internal 

diameter of a drill pipe is not large enough to fit the optimal number of typical 

navigation sensors, one prior system removed the drill bit from the borehole 

and lowered a monitoring tool down the borehole to determine its location. 

However, it is costly to stop drilling and spend time removing the drill bit to 

take measurements with the monitoring tool. Other systems used single-axis 

accelerometers to determine the vertical orientation of the drill bit. However, 

an accelerometer system cannot determine north, which is necessary to determine 

the full location of a borehole. Another prior design used magnetometers 

to determine the magnetic field direction from which the direction of north is 

approximated. However, such systems must correct for magnetic interference 

and magnetic materials used in the drill pipe and can suffer accuracy degradation 

due to the Earth’s changing magnetic field. 

This patent describes a novel navigation borehole system that can determine 

position and attitude for any orientation in a borehole using multiple gimbals 

that contain solid-state or other gyros and accelerometers. The navigation system 

includes a housing that can be placed within the smaller diameter drill pipes 

used toward the bottom of a borehole, an outer gimbal connected to the housing, 

and at least two or more stacked inner gimbals nested in and connected to 

the outer gimbal. The inner gimbals each have an axis parallel to one another 

and perpendicular to the outer gimbal. The inner gimbals contain electronic 

circuits, gyros, and accelerometers whose input axes span three-dimensional 

space. The system includes outer and inner gimbal drive systems to maintain 

the gyro and accelerometer input axes as substantially orthogonal triads and a 

processor that is responsive to the gyro accelerometer circuits to determine the 

attitude and the position of the housing in the borehole. 

This borehole navigation system can average out navigation errors due to gyro 

and accelerometer bias, gyro scale factor, and input-axis alignment errors, and 

allows gyro and accelerometer bias and gyro scale-factor calibration as well as 

attitude determination during gyrocompassing. This invention also provides 

long-term performance accuracy with only short-term requirements on sensor 

accuracy, can determine position and attitude while drilling, when the drill 

bit is stopped, when the drill bit is inserted or withdrawn, as well as while 

logging, both descending and ascending on a log line after the drill bit has been 

withdrawn.

Multi-Gimbaled Borehole Navigation System 77

ios 

Richard T. Martorana is a Distinguished Member of the Technical 

Staff and the Technical Director for the WASP Program. With 

over 39 years of research, design, and development experience, 

he has directed and managed programs for NASA, USAF, DARPA, 

NAVSEA, and others. He was responsible for the thermal design 

of the Trident II inertial measurement unit (IMU). His responsibilities 

have included: Section Chief for Fluid Mechanics and 

Thermal Engineering, Division Manager for Mechanical Design 

and Analysis, and Director of Systems Integration, Test, Evaluation, 

and Quality Management. He holds three U.S. patents in the areas of mechanical and thermal design. Mr. 

Martorana has BS and MS degrees in Mechanical Engineering from Columbia University and MIT, respectively, an 

MBA focused on management of innovation from Northeastern University, and he is a graduate of Harvard Business 

School’s Program for Management Development. 

Mitchell L. Hansberry is a Senior Member of the Technical Staff and a Mechanical Design Engineer with 25 years 

experience at Draper Laboratory. Specializing in the development of hardware configurations to solve system-level 

problems, he has been the Lead Mechanical Designer on many projects involving navigation instruments and 

systems, space hardware, and biomedical mechanisms. He has a BS in Mechanical Engineering from SUNY at Stony 

Brook. 

Michael E. Ash was a Principal Member of the Technical Staff in the System Integration, Evaluation, and Test Division, 

where he worked on inertial sensor and system modeling, simulation, and testing. Previously, he worked at 

the MIT Lincoln Laboratory on an interplanetary radar test of general relativity and on-satellite orbit determination. 

He was Chair of the Accelerometer Committee of the IEEE/Aerospace Electronics System Society (AESS) Gyro and 

Accelerometer Panel and an Associate Fellow of the AIAA. He received a BS from MIT and a PhD from Princeton 

University, both in Mathematics. 

78 Multi-Gimbaled Borehole Navigation System 

(l-r) Mitchell L. Hansberry 

and Richard T. Martorana

Flexural Plate Wave Sensor 

Patent # 7,109,633 B2 Date Issued: September 19, 2006 

Marc S. Weinberg, Brian T. Cunningham, Eric M. Hildebrandt 

This patent describes an improved flexural plate wave (FPW) sensor 

that includes a thin flexural plate with drive teeth disposed across 

its entire length. Further improvements associated with drive combs 

of varying tooth length are described. This improved FPW sensor 

reduces the number of eigenmodes excited in the flexural plate and outputs a 

single pronounced peak or a peak much larger than any of the other peaks and a 

distinct phase. This distinct peak simplifies the operating and designing associated 

drive and sense electronics and improves stability by eliminating erroneous 

readings due to interference created by mode hopping between eigemnodes. 

The FPW sensor includes a diaphragm or plate that is driven so that it oscillates 

at frequencies determined by a comb pattern and the flexural plate geometry. 

The comb pattern is disposed over the flexural plate and establishes electric 

fields that interact with the plate’s piezoelectric properties to excite motion. 

The eigenmodes describe the diaphragm displacements, which exhibit spatially 

distributed peaks. Each eigenmode consists of n half sine periods along the 

diaphragm’s length. A typical FPW sensor can be excited to eighty or more 

eigenmodes. In a typical FPW eigenmode, the plate deflection consists of many 

sinusoidal (or nearly sinusoidal) peaks. 

Previous flexure plate wave sensor designs typically include drive combs at one 

end of the plate and sense combs at the other end. The drive combs of these 

devices typically cover only 25% to 40% of the total plate length. When the 

number of drive teeth is small compared to the number of eigenmodes peaks, 

the small number of drive teeth can align with several eigenmodes. Not only are 

the eigenmodes perfectly aligned with the comb teeth excited, but other eigenmodes 

are also excited. In signal processing and spectral analysis, this effect is 

known as leakage. The increased number of eigenmodes excited in the FPW 

sensor produces a series of resonance peaks of similar amplitude and irregular 

phase, increasing design complexity and the operation of such FPW sensors. 

Other previous FPW designs employ drive and sense combs at opposite ends 

of the flexural plate and rely on analysis based on surface acoustic waves (SAW) 

where the waves propagate away from the drive combs and toward the sense 

combs, and back reflections are regarded as interference. A disadvantage is that 

SAW theory does not account for the sensor’s numerous small peaks and the 

electronics’ locking onto different eigenmodes depending on noise or starting 

conditions. 

Bioscale has licensed the FPW technology from Draper and will introduce a 

commercial product. 

Flexural Plate Wave Sensor 79

80 Flexural Plate Wave Sensor

ios 

(l-r) Eric M. Hildebrant and 

Marc S. Weinberg 

Marc S. Weinberg is a Laboratory Technical Staff Member at 

Draper Laboratory. He has been responsible for the design and 

testing of a wide range of traditional micromechanical gyroscopes, 

accelerometers, hydrophones, microphones, angular displacement 

sensors, chemical sensors, and biomedical devices. He served in 

the United States Air Force at the Aeronautical System Division, 

Wright-Patterson Air Force Base during 1974 and 1975, where 

he applied modern and classical control theory to design turbine 

engine controls, and at the Air Force Institute of Technology, where 

he taught gas dynamics and feedback control. He holds 25 patents 

with 12 additional in application. He has been a member of ASME 

since 1971. Dr. Weinberg received BS (1971), MS (1971), and 

PhD (1974) degrees in Mechanical Engineering from MIT where 

he held a National Science Foundation Fellowship. 

Brian T. Cunningham was a Principal Member of the Technical Staff at Draper Laboratory. Currently, he is an Associate Professor 

of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, where he is the Director of 

the Nano Sensors Group. His group focuses on the development of photonic crystal-based transducers, plastic-based fabrication 

methods, and novel instrumentation approaches for label-free biodetection. He is a founder and the Chief Technical 

Officer of SRU Biosystems (Woburn, MA), a life science tools company that provides high sensitivity plastic-based optical 

biosensors, instrumentation, and software to the pharmaceutical, academic research, genomics, and proteomics communities. 

Prior to founding SRU Biosystems in June 2000, he was the Manager of Biomedical Technology at Draper Laboratory, 

where he directed R&D projects aimed at utilizing defense-related technical capabilities for medical applications. He also 

served as Group Leader for MEMS sensors at Draper. Concurrently, he was an Associate Director of the Center for Innovative 

Minimally Invasive Therapy (CIMIT), a Boston-area medical technology consortium, where he led the Advanced Technology 

Team on Microsensors. Before joining Draper, he spent 5 years at the Raytheon Electronic Systems Division. Dr. Cunningham 

earned BS, MS, and PhD degrees in Electrical and Computer Engineering at the University of Illinois. 

Eric M. Hildebrant is a Principal Member of the Technical Staff. Initially, he worked on the MK6 CCD stellar sensor system. 

Later work focused on developing electronic integrated circuitry for micromechanical gyros, accelerometers, and chemical 

sensors. He holds four patents in the field of instrumentation. He received SB (1976), SB (1982), and MS (1989) degrees in 

Life Sciences, Electrical Engineering, and Engineering Design from MIT and Tufts University. 

Flexural Plate Wave Sensor 81

82 2006 Patents Issued 

patents 

2006 

Issued 

Anderson, J.M.; Kerrebrock, P.A.; McFarland, W.W.; 

Ogrodnik, T.G. 

Crawler Device 

Patent Number 7,137,465 B1, November 21, 2006 

Antkowiak, B.M.; Carter, D.J.; Duwel, A.E.; Mescher, 

M.J.; Varghese, M.; Weinberg, M.S. 

MEMS Piezoelectric Longitudinal Mode Resonator 

Patent Number 7,005,946 B2, February 28, 2006 

Coskren, W.D.; Parry, J.R.; Williams, J.R.; Sebelius, 

P.W. 

Sensor Apparatus and Method of Using Same 

Patent Number 7,100,689 B2, September 5, 2006 

Elliott, R.D.; Ward, P.A. 

Apparatus for and Method of Sensing a Measured 

Input 

Patent Number 7,055,387 B2, June 6, 2006 

Greenspan, R.L.; Przyjemski, J.M. 

Method and System for Implementing a Communications 

Transceiver Using Modified GPS User 

Equipment 

Patent Number 7,123,895 B2, October 17, 2006 

Hansberry, M.L.; Ash, M.E.; Martorana, R.T. 

Multi-Gimbaled Borehole Navigation System 

Patent Number 7,093,370 B2, August 22, 2006 

Miller, R.A.; Nazarov, E.G.; Eiceman, G.A.; Krylov, E. 

Method and Apparatus for Electrospray Augmented 

High Field Asymmetric Ion Mobility Spectrometry 

Patent Number 7,075,068 B2, July 11, 2006 

Miller, R.A.; Nazarov, E.G.; Zapata, A.M.; Davis, 

C.E.; Eiceman, G.A.; Bashall, A.D. 

Systems for Differential Ion Mobility Analysis 

Patent Number 7,057,168 B2, June 6, 2006 

Robbins, W.L.; Miller, R.A. 

Spectrometer Chip Assembly 

Patent Number 7,098,449 B1, August 29, 2006 

Weinberg, M.S.; Cunningham, B.T.; Hildebrant, E.M. 

Flexural Plate Wave Sensor 

Patent Number 7,109,633 B2, September 19, 2006 

Williams, J.R.; Cunningham, B.T. 

Flexural Plate Wave Sensor and Array 

Patent Number 7,000,453 B2, February 21, 2006 

Williams, J.R.; Dineen Jr., D.A.; Prince J.R. 

Microfluidic Ion-Selective Electrode Sensor System 

Patent Number 7,101,472 B2, September 5, 2006

The 

performance 

2006 Draper Distinguished 

Awards 

DPA Screening Committee 

Members 

The DPA was established in 1989 

and is the most prestigious award 

that Draper bestows for extraordinary 

achievements by individuals 

or teams. These achievements must 

constitute a major technical accomplishment, 

the technical effort must 

entail highly challenging work of 

substantial benefit to the Laboratory 

and the outside community, 

include a recent discrete accomplishment 

that is clearly extraordinary 

and represents a standard 

of excellence for the Laboratory, 

and the responsible individual or 

core team can be identified as the 

prime participant(s) in achieving 

the significant results. This year’s 

committee was chaired by Scott 

Uhland. Members included Heather 

Clark, Christopher Gibson, Lauren 

Kessler, Edward Lanzilotta, David 

Owen, Dora Ramos, Elliot Ranger, 

and Roger Wilmarth. Administrative 

support was provided by Noel 

Cassidy. 

Chairman of the Board John R. Kreick and then-President Vincent Vitto presented 

the 2006 Draper Distinguished Performance Awards (DPAs) to a team and to an 

individual at the Annual Dinner of the Corporation on October 4, 2006. 

Accelerated Delivery of Miniaturized Radio Frequency Communications 

Hardware 

The Next Generation Fastraker 

team members responsible for 

hardware achieved production 

qualification of the first engineering 

model, which was the first 

mixed-signal multichip module 

ever qualified for production by 

Draper. Production qualification 

occurred earlier than scheduled 

and in a package so much smaller 

than the sponsor’s specifications 

that the overall system size was 

reduced by nearly a factor of 

three. 

Development and Strategic Distribution of a Geospatial Intelligence 

Networked System to Middle Eastern Military Force 

Harold A. Bussey led the team 

that adapted the Draper-developed 

U.S. Air Force system for 

handling geospatial information 

for use by NATO forces in 

the Middle East. He delivered 

the system to users in the field 

and trained them in its use. The 

system’s usefulness has led other 

military organizations to consider 

adopting it. 

(clockwise from left) Michael T. Clohecy, Vincent J. Attenasio, 

Jr., Don A. Black, Michael J. Matranga, John R. Burns III, 

Donald I. Schwartz, and (inside center) Valerie H. Lowe 

(l-r) President James D. Shields, Award Recipient Harold 

A. Bussey, and Chairman of the Board John R. Kreick 

The 2006 Draper Distinguished Performance Awards 83

Sir Timothy Berners-Lee 

84 The 2007 Charles Stark Draper Prize 

draper 

The 2007 Charles Stark 

Prize 

The Charles Stark Draper Prize was established in 1988 to 

honor the memory of Dr. Charles Stark Draper, “the father 

of inertial navigation.” Awarded annually, the Prize was 

instituted by the National Academy of Engineering (NAE) 

and endowed by Draper Laboratory. It is recognized as one 

of the world’s preeminent awards for engineering achievement 

and honors individuals who, like Dr. Draper, developed 

a unique concept that has contributed significantly to 

the advancement of science and technology and the welfare 

and freedom of society. 

The 2007 Charles Stark Draper Prize was presented to Sir Timothy 

Berners-Lee at a ceremony on February 20 in Washington, 

D.C. According to the NAE, Berners-Lee “imaginatively 

combined ideas to create the World Wide Web, an extraordinary 

innovation that is rapidly transforming the way people store, access, 

and share information around the globe. Despite its short existence, 

the Web has contributed greatly to intellectual development and plays 

an important role in health care, environmental protection, commerce, 

banking, education, crime prevention, and the global dissemination of 

information.” In addition, he “demonstrated a high level of technical 

imagination in inventing this system to organize and display information 

on the Internet.” His innovations include the uniform resource identifier 

(URI), HyperText Markup Language (HTML), and HyperText Transfer 

Protocol (HTTP). 

Photo credit: Bill Truslow 

Berners-Lee proposed his concept 

for the Web in 1989 while at the 

European Organization for Nuclear 

Research (CERN), launched it on the 

Internet in 1991, and continued to 

refine its design through 1993. He 

designed the Web with public domain 

scalable software and an open architecture 

to allow other inventions to 

be built on it. 

Berners-Lee is currently a senior 

researcher and holder of the 3Com 

Founders Chair at the Computer 

Science and Artificial Intelligence 

Laboratory at MIT and a professor 

of computer science in the School of 

Electronics and Computer Science 

at the University of Southampton, 

UK. He continues to guide the Web’s 

evolution as founder and director 

of the World Wide Web Consortium 

(W3C), an international forum 

that develops standards for the 

Web. A graduate of Oxford University, 

England, he became a fellow of 

the Royal Society in 2001. He has 

received several international awards, 

including the Japan Prize, the Prince 

of Asturias Foundation Prize, the 

Millennium Technology Prize, and 

Germany’s Die Quadriga Award. 

Berners-Lee was knighted by Queen 

Elizabeth in 2004. He is the author of 

“Weaving the Web.”

Recipients of the Charles Stark Draper Prize 

2006: Willard S. Boyle and George E. Smith for the invention of the charge-coupled device (CCD) 

2005: Minoru Araki, Francis J. Madden, Don H. Schoessler, Edward A. Miller, and James W. Plummer 

for their invention of the Corona earth-observation satellite technology 

2004: Alan C. Kay, Butler W. Lampson, Robert W. Taylor, and Charles P. Thacker for the development 

of the world’s first practical networked personal computers 

2003: Ivan A. Getting and Bradford W. Parkinson for their technological achievements in the development 

of the Global Positioning System 

2002: Robert S. Langer for bioengineering revolutionary medical drug delivery systems 

2001: Vinton Cerf, Robert Kahn, Leonard Kleinrock, and Lawrence Roberts for their individual 

contributions to the development of the Internet 

1999: Charles K. Kao, Robert D. Maurer, and John B. MacChesney for development of fiber-optic 

technology 

1997: Vladimir Haensel for the development of the chemical engineering process of “Platforming” 

(short for Platinum Reforming), which was a platinum-based catalyst to efficiently convert 

petroleum into high-performance, cleaner-burning fuel 

1995: John R. Pierce and Harold A. Rosen for their development of communication satellite 

technology 

1993: John Backus for his development of FORTRAN, the first widely used, general-purpose, highlevel 

computer language 

1991: Sir Frank Whittle and Hans J.P. von Ohain for their independent development of the turbojet 

engine 

1989: Jack S. Kilby and Robert N. Noyce for their independent development of the monolithic integrated 

circuit 

For information on the nominating process, contact the Awards Office at the National 

Academy of Engineering at (202) 334-1266 or http://www.nae.edu/awards. 

The 2007 Charles Stark Draper Prize 85

Laura Forest 

The 2006 Howard Musoff Student Mentoring Award was presented to 

Laura Forest, a Human-System Collaboration Engineer in the Software 

System Architectures and Human-Computer Interfaces (HCI) Department. 

When asked about the importance of mentoring activities, Laura 

remarked, “It has been very rewarding to mentor and work with Draper Laboratory 

Fellows (DLF) and other student interns. I have especially enjoyed witnessing the 

students’ transformation as they step from undergraduate classroom-based problem 

solving to the broader scope of engineering research and subsequent publishing. 

Seeing the students take the knowledge and experience I share with them and 

use it for their own growth is truly fulfilling. Mentoring can also establish life-long 

contacts and friendships – I’m planning on attending one of my former DLF’s 

wedding in Reno, NV, this summer. Additionally, the students contribute to my 

own professional development through the research areas they explore, the leadership 

opportunities they present, and the associated expansion of my academic 

contacts. I look forward to continuing mentoring relationships in the future.” 

86 The 2006 Howard Musoff Student Mentoring Award 

mentoring 

The 2006 Howard Musoff Student 

Award 

In addition to her mentoring activities at 

Draper, for the past two years, Laura has 

been a volunteer with Science Club for 

Girls, a weekly after-school program in 

Cambridge. Volunteers perform a variety 

of science experiments with the girls and 

discuss their careers as scientists. 

Laura’s primary research interests include 

cognitive engineering, human-guided 

algorithms, human factors, and HCI. She is 

currently working on projects that include 

research on human-guided algorithms, 

spacecraft automation for lunar landing, 

decision support for intelligence analysts, 

and requirements for facial recognition 

systems. A member of the Human Factors 

and Ergonomics Society (HFES), Society of 

Women Engineers (SWE), IEEE, and AIAA, 

Laura has a BS in Industrial and Systems 

Engineering from Georgia Tech and an MS 

in Aeronautics and Astronautics from MIT. 

The Howard Musoff Mentoring Award 

was established in his memory in 2005. 

A Draper employee for more than 40 

years, Musoff advised and mentored 

many Draper Fellows. This award is given 

each February during National Engineers 

Week and recognizes staff members who, 

as Musoff did, share their expertise and 

supervise the professional development 

and research activities of Draper Fellows. 

The award, endowed by the Howard 

Musoff Charitable Foundation, includes 

a $1,000 honorarium and a plaque. Each 

Engineering Division Leader may submit 

one nomination of a staff person from his 

Division. The Education Office assists in 

the process by soliciting comments from 

students who were residents during that 

time period. The Selection Committee 

consists of the Vice President of Engineering, 

the Principal Director of Engineering, 

and the Director of Education.

esearch 

2006 Graduate 

Theses 

During 2006, the Draper Fellow Program served 65 students from MIT and several other universities. Abstracts of theses 

completed this year are available on the Laboratory’s web site at www.draper.com. The list of completed theses follows: 

Anderson, A.D.; Supervisors: Gustafson, D.E.; Deyst, J. 

Recovering Sample Diversity in Rao-Blackwellized 

Particle Filters for Simultaneous Localization and 

Mapping 

Master of Science Thesis, MIT, June 2006 

Bairstow, S.H.; Supervisors: Barton, G.H.; Deyst, J.J. 

Reentry Guidance with Extended Range Capability for 

Low L/D Spacecraft 

Master of Science Thesis, MIT, February 2006 

Barker, D.R.; Supervisors: Singh, L.; How, J. 

Robust Randomized Trajectory Planning for Satellite 

Attitude Tracking Control 


Beaton, J.S.; Supervisors: Dever, C.W.; Appleby, B.D. 

Human Inspiration for Autonomous Vehicle Tactics 

Master of Science Thesis, MIT, May 2006 

Bryant, C.H.; Supervisors: Armacost, A.P.; Abramson, 

M.R.; Kolitz, S.E.; Barnhart, C. 

Robust Planning for Effects-Based Operations 


Chau, D.; Supervisors: Racine, R.J.; Liskov, B. 

Authenticated Messages for a Real-Time Fault-Tolerant 

Computer System 

Master of Engineering Thesis, MIT, September 2006 

Earnest, C.A.; Supervisors: Dai, L.; Page, L.A.; Roy, N.; 

Barnhart, C. 

Dynamic Action Spaces for Autonomous Search 

Operations 

Master of Science Thesis, MIT, March 2006 

Harjes, D.I.; Supervisors: Clark, H.A.; Kamm, R.D. 

High Throughput Optical Sensor Arrays for Drug 

Screening 

Master of Science Thesis, MIT, September 2006 

Jimenez, A.R.; Supervisors: Kaelbling, L.P.; DeBitetto, P.A. 

Policy Search Approaches to Reinforcement Learning 

for Quadruped Locomotion 

Master of Engineering Thesis, MIT, May 2006 

Krenzke, T.P.; Supervisors: McConley, M.W.; Appleby, B.D. 

Ant Colony Optimization for Agile Motion Planning 


McAllister, D.B.; Supervisors: Kahn, A.C.; Kaelbling, L.P.; 

Jaillet, P. 

Planning with Imperfect Information: Interceptor 

Assignment 


Mihok, B.E.; Supervisors: Miller, J.W.; Appleby, B.D. 

Property-Based System Design Method with Application 

to a Targeting System for Small UAVs 


Parikh, K.M.; Supervisors: Weinberg, M.S.; Freeman, D.M. 

Modeling the Electrical Stimulation of Peripheral 

Vestibular Nerves 

Master of Engineering Thesis, MIT, September 2006 

Ren, B.B.; Supervisors: Keshava, N.; Freeman, D. 

Calibration, Feature Extraction and Classification of 

Water Contaminants Using a Differential Mobility 

Spectrometer 

Master of Engineering Thesis, MIT, May 2006 

Sakamoto, P.; Supervisors: Armacost, A.P.; Kolitz, S.E.; 

Barnhart, C. 

UAV Mission Planning Under Uncertainty 


Schaaf, B.T.; Supervisors: Andrews, G.L.; Appleby, B.D. 

Using Learning Algorithms to Develop Dynamic Gaits 

for Legged Robots 


Smith, C.A.; Supervisors: Cummings, M.L.; Forest, L.M. 

Ecological Perceptual Aid for Precision Vertical 

Landings 


Smith, T.B.; Supervisors: Nervegna, M.F.; Barnhart, C. 

Decision Algorithms for Unmanned Underwater 

Vehicles During Offensive Operations 


Springmann, P.N.; Supervisors: Proulx, R.J.; Deyst, J.J. 

Lunar Descent Using Sequential Engine Shutdown 

Master of Science Thesis, MIT, January 2006 

Sterling, R.M.; Supervisors: Racine, R.J.; Liskov, B.H. 

Synchronous Communication System for a Software- 

Based Byzantine Fault-Tolerant Computer 

Master of Science Thesis, MIT, August 2006 

Swanton, D.R.; Supervisors: Brown, R.A.; Kaelbling, L.P. 

Integrating Timeliner and Autonomous Planning 

Master of Science Thesis, MIT, August 2006 

Teahan, G.O.; Supervisors: Paschall II, S.C.; Battin, R.H. 

Analysis and Design of Propulsive Guidance for Atmospheric 

Skip Entry Trajectories 


Thrasher, S.W.; Supervisors: Dever, C.W.; Deyst, J.J. 

Reactive/Deliberative Planner Using Genetic Algorithms 

on Tactical Primitives 


Varsanik, J.S.; Supervisors: Duwel, A.E.; Kong, J-A 

Design and Analysis of MEMS-Based Metamaterials 

Master of Engineering Thesis, MIT, June 2006 

2006 Graduate Research Theses 87

2006 

technology 

Exposition 

Each year, Draper hosts a Technology Exposition (Tech 

Expo) to showcase recent projects and highlight the 

Laboratory’s core competencies. Held on October 

4-5 to coincide with the fall meeting of Draper’s 

Board of Directors and the Annual Meeting of the Corporation, 

guests included employees and Corporation members, 

students from local universities and Cambridge public schools, 

and sponsors. 

The exhibits featured developing technologies in the Laboratory’s 

program areas: strategic, tactical, space systems, special 

operations, biomedical engineering, and independent research 

and development. The exhibits also reflected the Laboratory’s 

core competencies: guidance, navigation, and control; embedded, 

real-time software; microelectronics and packaging; 

autonomous systems; distributed systems; microelectromechanical 

systems; biomedical engineering; and prototyping 

system solutions. In coordination with Draper’s Education 

Office, many projects also included graduate or undergraduate 

students on their teams. 

Draper’s subsidiary venture capital fund, Navigator Technology 

Ventures, LLC (NTV), displayed information about a number 

of its portfolio companies. These companies include Actuality 

Systems, Aircuity, Assertive Design, Food Quality Sensor (FQS) 

International, HistoRx, Polnox Corp., Polychromix, Renalworks 

Medical Corp., Sionex Corp., and Tizor Systems. 

Linda Fuhrman shares her enthusiasm for space 

exploration and Draper’s role with Cambridge 

public school students. 

88 2006 Technology Exposition 

Ray Barrington (left) and Stephen Smith 

(center) discuss Draper’s Space Programs 

with an interested visitor. 

Malinda Tupper demonstrates one of several 

biological/chemical sensors under development 

as Draper continues to pursue the 

smallest, most robust, and selective electronic 

detection platforms. 

Roger Wilmarth (left) and a Draper Fellow 

discuss innovations in small robotics systems 

for surveillance and rescue operations, including 

precision airdrop systems, small undersea 

vehicles, and systems designed to overcome 

difficult mobility challenges.

#* 

The Charles Stark Draper Laboratory, Inc. 

555 Technology Square 

Cambridge, MA 02139-3563 

Phone: (617) 258-1000 

www.draper.com 

Business Development 

busdev@draper.com 

Phone: (617) 258-2124 

Washington 

Suite 501 

1555 Wilson Boulevard 

Arlington, VA 22209 

Phone: (703) 243-2600 

Houston 

Suite 470 

17629 El Camino Real 

Houston, TX 77058 

Phone: (281) 212-1101

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