05565507

8/7/2019 05565507

1/8

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010 2521

A Low-Power Shoe-Embedded Radar forAiding Pedestrian Inertial Navigation

Chenming Zhou , Member, IEEE, James Downey , Student Member, IEEE,Daniel Stancil, Fellow, IEEE, and Tamal Mukherjee, Member, IEEE

AbstractNavigation in global positioning system (GPS)-deniedor GPS-inhibited environments such as urban canyons, mountainareas, and indoors is often accomplished with an inertial measure-ment unit (IMU). For portable navigation, miniaturized IMUssuffer from poor accuracy due to bias, bias drift, and noise. Wepropose to use a low-power shoe-embedded radar as an aidingsensor to identify zero velocity periods during which the individualIMU sensor biases can be observed. The proposed radar sensorcan also be used to detect the vertical position and velocity of theIMU relative to the ground in real time, which provides additionalindependent information for sensor fusion. The impacts of thenoise and interference on the system performance have beenanalyzed analytically. A prototype sensor has been constructed todemonstrate the concept, and experimental results show that theproposed sensor is promising for position and velocity sensing.

Index TermsDirect conversion, inertial navigation, positionand velocity sensor, zero velocity update (ZUPT).

I. INTRODUCTION

WHILE THE global positioning system (GPS) is typi-

cally used in current navigation systems for pedestrians,

alternative techniques still need to be developed for environ-ments such as indoors, underground, urban canyons, and

mountain areas where GPS signals are degraded or unavailable.

Pedestrian tracking in GPS-denied environments is often ac-

complished with inertial navigation sensors since they operate

independently of external assets and without prior knowledge

of the environment. Recent improvements in microelectrome-

chanical systems (MEMS) have made possible low-power

shoe-mounted inertial sensors for pedestrian tracking [1][3].

However, an inertial measurement unit (IMU) equipped only

with accelerometers and gyroscopes does not provide accept-

able accuracy owing to accumulated integration errors from

unknown sensor biases [4].

Manuscript received December 23, 2009, revised May 15, 2010; acceptedJune 03, 2010. Date of publication September 07, 2010; date of current versionOctober 13, 2010. This work was supported by the Air Force Research Labora-tory(AFRL) and by the Defense AdvancedResearchProjects Agency (DARPA)under Agreement FA8650-08-1-7824.

C. Zhou, J. Downey, and T. Mukherjee are with the Department of Electricaland Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213USA (e-mail: [email protected]; [email protected]; [email protected]).

D. Stancil was with the Department of Electrical and Computer Engineering,Carnegie Mellon University, Pittsburgh, PA 15213 USA. He is now with theElectrical and Computer Engineering Department, North Carolina State Uni-versity, Raleigh, NC 27695 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMTT.2010.2063810

A technique known as zero velocity update (ZUPT) has been

applied to reduce the accumulated error [1]. ZUPTing systems

require a mechanism to measure when the velocity of the IMU

is zero. While estimating zero velocity from the IMU data itself

provides some improvement, an independent means for directly

determining the time interval over which the ZUPT can take

place is preferred.

To address this challenge, we propose to use a compact shoe-

embedded radarterrain relative velocity (TRV) radaras an

aiding sensor to improve the accuracy of a MEMS-based iner-

tial navigation system [5]. In addition to estimating ZUPTs, theproposed TRV sensor may also be used for accurately detecting

the position and velocity of the IMU relative to the ground in the

vertical direction in real time, adding independent information

for sensor fusion.

The principle of the proposed TRV sensor is based on contin-

uous wave (CW) radar that compares the RF source phase with

the ground reflected wave phase. The phase difference is pro-

portional to distance. We have implemented this concept using

connectorized modular commercial off-the-shelf (COTS) com-

ponents. The preliminary results show that the proposed RF mo-

tion sensor is promising for identifying the timing and duration

of a stance phase, independent of an IMU. A design constraintof this sensor is that it must be small enough to be embedded

into a shoe. Low power consumption is also a desirable feature

since it will be powered by a battery.

RF sensing of zero velocity is chosen over other sensing

mechanisms such as optical and acoustic waves because of its

relative insensitivity to the external environment. A similar

mechanism has been used for remote monitoring of vital signs

[6].

II. SYSTEM WORKING PRINCIPLE ANDPERFORMANCE ANALYSIS

A. Working Principle

The system block diagram of the proposed TRV sensor is

shown in Fig. 1. A single signal source provides both the RF

output and local oscillator (LO) signals, through a two way-0

power splitter (the 1:2 block shown in Fig. 1). The LO signal

split from the source is further divided into two branches with a

phase difference of 90 . These two orthogonal LO signals then

mix with RF signals from the receive antenna and produce two

IF signals (here at zero frequency). A power amplifier (PA) and

a low-noise amplifier (LNA) are added to the system to increase

the signal-to-noise ratio (SNR). A direct conversion scheme has

been employed due to the following reasons:

low complexity and low power consumption;

0018-9480/$26.00 2010 IEEE

8/7/2019 05565507

2/8

2522 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

Fig. 1. Shoe-embedded radar: system block diagram.

Fig. 2. Distance illustration of a shoe-embedded radar sensor.

small size;

elimination of image-rejection issue;

reduced requirement on the phase noise of the VCO since

a single oscillator is used to measure the distance.

However, it is known that a direct conversion receiver suffers

from dc offsets caused by interfering signals that are in-band to

the receiver [7], [8]. DC offset and its impacts on the system

performance will be addressed in Section II-C.

Let denote the single-tone signal generated by the

signal source, where is the angular frequency. The LO signal

for the in-phase channel mixer can be represented as

(1)

where and are the amplitude and phase of the LO signal,

respectively. The RF signal before the mixer can be written as

(2)

where is the amplitude of the RF signal, is the speed of

light, and is a constant phase delay. Here, represents half

of the path length that a signal travels when it is emitted from

the transmit antenna, reflected by the ground, and finally de-

tected by the receive antenna. The two antennas (RX and TX)

are mounted on the same antenna plate with a separation dis-

tance of , as shown in Fig. 2. Let denote the distance be-

tween the antenna plate and ground plane, given by

(3)

For the RF motion sensor proposed in this paper, the antenna

plate will be embedded in the heel of the shoe and gives theelevation of the heel.

The dc component output from the channel in-phase/quadra-

ture (I/Q) of the sensor is

(4)

where , and . Here,

is the gain of the mixer and .

Therefore, given measured voltages and , an estimate

of the path length can be reconstructed from

(5)

where is the estimated path length and is an integer to

compensate for the phase ambiguity caused by the inverse tan-

gent operation. If the sensor always starts with a stance phase

with a known initial path length , the unknown phase in

(5) can be removed

(6)

It should be noted that phase unwrapping should be considered

in (6) if . The velocity can then be obtained by

differentiating the path length with respect to time

(7)

The vertical velocity relative to ground is calculated by

(8)

At large distances where , we have , and

.

The inconvenience of transforming to can be avoided

by replacing the two antennas in Fig. 1 with a single antenna.

Transmit signals and receive signals could share the same an-

tenna through a directional coupler or a circulator. in this case,

we have so that and . However, isolation

between the transmitter and receiver could be more challenging.

B. System Noise Analysis

Equation (6) assumes an ideal system where noise is absent.

However, for a practical system, noise disturbances must betaken into account [9]. In this section, we will investigate how

noise presented in the system affects the distance and velocity

reconstructions.

The received noise-corrupted RF signal can be represented

with a vector notation as , where

and denote the signal and noise vectors, respec-

tively. In the I/Q plane shown in Fig. 3, the random noise vector

is added onto the signal vector with a uniformly distributed

random phase , and a random amplitude based on a prob-

ability distribution.

As a result from the noise vector, the amplitude and phase of

the corrupted signal randomly change over time. Let ,

and denote the phase reconstruction error dueto the noise disturbance. Given a fixed and signal vector ,

8/7/2019 05565507

3/8

ZHOU et al.: LOW-POWER SHOE-EMBEDDED RADAR 2523

Fig. 3. Impact of SNR on the distance reconstruction.

the phase estimation error varies with . The noise vector

forms a circle in the I/Q plane, as shown in Fig. 3, as

randomly changes. It is apparent that reaches its maximum

value when is tangential to the circle of with a maximum

value of

(9)

Considering additive Gaussian noise with a zero mean and a

standard deviation of , it is known that the possibility for

is 95.4%. Let . The corresponding max-

imum distance estimation error (with 95.4% confidence) is

(10)

For high SNR, we have the approximation

(11)

It is shown by simulation that the above approximation only

introduces 1% position error with an SNR of 15 dB. Therefore,

the above approximation is valid for most practical TRV sensor

analyses.

According to (11), the system positioning accuracy only de-

pends on two factors: operating frequency and system SNR. An

increase of SNR and/or results in better positioning accuracy.

Another application of (11) is to estimate the required min-

imum SNR to meet a target position resolution, assuming a

noise-limited system. As an example, for our system with an

operating frequency GHz, a positioning resolution of

1 mm requires the system SNR to be greater than 14 dB.If the velocity is sufficiently low such that the distance of a

sensor moved within two samples separated by is less than

the above minimum distance error , the system cannot

give a reliable velocity estimation. Therefore, the position ac-

curacy in (11) also sets a lower limit for the velocity that can

be detected by the sensor. This minimum detectable velocity is

simply determined by

(12)

where is the wavelength. For example, considering

Hz, dB, and ms, a minimumdetectable velocity of 5.08 mm/s can be obtained based on (12).

Fig. 4. Impact of SIR on the distance reconstruction.

It should be noted that can be greatly decreased by re-

ducing the bandwidth of the system until .

C. Impact of Interference on the System Performance

Besides the desired RF signal, which is reflected by theground, sometimes other undesirable in-band RF signals arepresent at the receiver. It should be noted that this interferencecould be from the RF source of the radar (coherent interference)or independent sources (noncoherent interference). Usually thepower of noncoherent interference is much lower comparedto coherent interference, depending on the system operatingfrequency. In this paper, we will focus on coherent interferenceand analyze its impact on the system performance. Theseinterfering signals will enter into the mixer and mix with the

LO signal, resulting in dc offsets at the output of the sensor.DC offset is one of the major issues caused by a direct con-version design and will have a significant impact on the systemperformance if there is no compensation for it. Several interfer-ence sources may contribute to the dc offset, including

multiple reflections between the antenna plate and ground,time variant, depending on the distance between the groundand antenna plate;

feed through due to poor isolation between Tx and Rx an-tennas [10], [11], time invariant;

insufficient LO-RF isolation [8], time invariant.We follow a similar procedure as in Section II-B and replace

the noise vector with a interference vector . To simplify

the problem, we assume the noise power in this scenario is verylow compared to interference and can be ignored. The receivedRF signal is then written as and the signal-to-interference ratio (SIR) is defined by . Notethat the interference has a phase of , which is not randomlychanging. Considering the triangle formed by the three vectorsand applying the law of sines, we have

(13)

where is the estimation error caused by interfer-ence . According to Fig. 4, we haveand . Therefore,

(14)

8/7/2019 05565507

4/8


Fig. 5. Distance comparison between the simulated result and the closed-formresult.

Substituting (14) into (13) and solving for yields

(15)

Recalling , the distance estimation error canbe expressed as

(16)We thus establish the relationship between the SIR and dis-

tance error in a closed form. Fig. 5 illustrates how the distance

reconstruction error changes with respect to the distancein wavelength. The closed-form results and the simulated resultsare calculated using (16) and (6), respectively, with a frequencyof 6.7 GHz.

As shown in Fig. 5, the closed-form results agree well withthe simulated results, implying our derivation in (16) is correct.Another observation in Fig. 5 is that varies periodically withdistance with a period of . The magnitude of the variationin increases as the value of the SIR decreases from 10 to 4dB. The relationship between the SIR and the maximum isgiven below.

In (16), vertices of occur when

(17)

with a maximum value of

(18)

If the SIR is large, (18) can be simplified by the small angleapproximation as

(19)

Equation (19) gives an estimate of how the distance accuracyis affected by an uncalibrated interference. As a quick example,

considering GHz, the maximum distance error causedby an interference with dB is about 1.2 mm.

The reconstructed velocity is obtained by directly differenti-ating (16) with respect to time , yielding

(20)

where . It is apparent that is timevariant even when the sensor is moving at a constant velocity.Let denote the velocity estimation error, thenwe have

(21)According to (21), increases with the velocity . In otherwords, an uncalibrated interference could introduce a large ve-locity estimation error when the sensor is moving at high speed.On the other hand, we have for , implying inter-ference has little impact on zero velocity sensing. Additionally,it can be found that repeats itself as the sensor moves everyhalf wavelength distance. This phenomena has been observed inour experimental results in Sections IV-A and IV-C.

D. System With Both Interference and Noise

When both interferences and noise are present in the system,

the distance estimation error is the summation of the individual

errors caused by noise and the interference

(22)

III. SYSTEM PROTOTYPING

To prove the concept, a TRV sensor prototype has been built

using COTS components, as shown in Fig. 6. A Mini-Circuits

ZX95-6740C voltage-controlled oscillator (VCO) is used as

the signal source. A potentiometer is added into the system to

provide a tuning voltage for the VCO according to the antenna

resonant frequency. A high system frequency is desirable since

higher frequencies allow the design of smaller antennas andalso provides better position resolution. The working frequency

of 6.7 GHz chosen in our prototype is a balance between the

antenna size and commercially available components. The two

mixers, quadrature hybrid, and 0 power splitter shown in Fig. 1

are integrated and implemented with a single-chip Hittite mono-

lithic microwave integrated circuit (MMIC) I/Q mixer module

(HMC520LC4) (labeled mixers in Fig. 6). All the components

are mounted in an 8.7 6.3 2 in aluminum box. Power con-

sumption of this TRV prototype is about 1 W.

The antenna design is a critical part of the shoe-based RF mo-

tion sensor. This application requires the antennas to be both

small and have low mutual coupling between transmit and re-

ceive antennas. This mutual coupling will contribute to the dcoffset during direct conversion and is thus undesirable. To make

8/7/2019 05565507

5/8

8/7/2019 05565507

6/8


Fig. 9.V

output from the TRV sensor. (a) OverallV

during the motiongiven in Section IV-A. (b) Zoomed-in version of the two voltage waveforms forthe first 4 s.

Fig. 10. Reconstructed position based on V given in Fig. 9.

change slightly with the distance . In other words, the dc off-

sets cannot be completely removed by prior calibration.

Fig. 11 shows the reconstructed velocity and detected zero

velocity periods. Velocities are reconstructed based on the dis-tances shown in Fig. 10 by (7) and (8). To remove the short-term

variations caused by the electronic noise in the system, a simple

arithmetic average (over 20 samples taken at a 1-kHz rate) has

been applied. Ground truth for the velocity is obtained by di-

rectly differentiating the computed position ground truth with

respect to time. As shown in Fig. 11, the reconstructed velocity

curve agrees well with the computed ground truth, except on

the part where the sensor is moving at a constant velocity. The

reconstructed velocity curve shows a variation with an ampli-

tude of about 20 mm/s when the sensor is moving at a con-

stant velocity. This variation is caused by the residual dc offset

after the calibration, as addressed in Section II-C. Zero velocity

periods are identified by monitoring the change of the recon-structed distances.

Fig. 11. Reconstructed velocity and detected zero velocity periods.

B. Stability Test

With the same experimental setup given in Section IV-A, a

stability test where antennas are set close to the reflector andremain static for 1 h was conducted. The motivation for the sta-

bility test is twofold: 1) to measure the distance sensing error

due to electronic drifts over a long time period and 2) to char-

acterize the system performance when the antenna is very close

to the reflector, simulating a scenario when shoes are in contact

with the ground.

For the stability test, the velocity of the stepper motor

was set to 25.4 mm/s (1 in/s) and the acceleration was

5.04 mm/s in/s . The initial position of the sensor was

measured as m. The motion of the stepper motor

was programmed in the following way:

1) stationary (1 s);

2) constant velocity forward 0.0762 m (3 in);

3) stationary (3600 s);

4) constant velocity backward 0.0762 m (3 in);

5) stationary (1 s).

The dc voltages (with offset calibrated) collected from the

I and Q channels over 1 h are shown in Fig. 12(a). The re-

constructed distance based on is shown in Fig. 12(b). The

ground truth distance computed based on the motion commands

sent to the stepper motor is also provided as a reference. As

shown in Fig. 12(b), the reconstructed distance curve agrees

well with the computed ground truth, implying our system still

performs well when antennas are close to a concrete reflector.

Fig. 12(c) gives a zoomed in version of Fig. 12(b). It can be ob-served from Fig. 12(c) that the distance drift caused by long-

time operation over 1 h is less than 1 mm.

C. Walking Test

A preliminary walking-in-place test was conducted to demon-

strate the functionality of the TRV sensor. Antennas were em-

bedded in the heel of a boot, as shown in Fig. 13. Except an-

tennas, the other components in Fig. 13 were placed on a nearby

table. Again, two RF cables were used to connect the antenna

and TRV box. For the experimental results reported here, the

walking area was restricted by the limited length of the two ca-

bles and the motion of the foot is up and down only. The reflec-tion interface is a typical flat concrete floor.

8/7/2019 05565507

7/8

ZHOU et al.: LOW-POWER SHOE-EMBEDDED RADAR 2527

Fig. 12. Long-term (1) position accuracy characterization of a TRV sensor.(a) V output from the TRV sensor. (b) Reconstructed distance based on mea-sured V in (a). (c) Zoomed-in version of (b).

Fig. 13. Experimental setup for walking test.

Fig. 14 shows the experimental results for the first three stepsof a total of 100 steps. Fig. 14(a) shows the collected dc voltages

during the walking, with dc offsets removed by prior cali-

bration. Fig. 14(b) shows the reconstructed distance between the

heel and ground. It can be clearly observed from Fig. 14(b) that

the foot starts from a stationary phase with a zero distance and

then experiences a motion phase where distance first increases

and then decreases. The distance goes back to zero when the

foot touches the ground and one step is accomplished. Again,

the velocity estimation of the motion can be obtained based on

detected distance by applying (8), and zero velocity periods can

be identified by monitoring the variation of the reconstructed

distance. The detected zero velocity periods and velocity are

shown in Fig. 14(c). In Fig. 14(c), correspondsto zero velocity true/false.

Fig. 14. Experimental results of a walking test with a TRV sensor embeddedinto the heel. (a) V output from the TRV sensor. (b) Reconstructed distancerelative to the ground. (c) Reconstructed velocity with respect to time as well asthe detected zero velocity periods of the shoe. Z U P T = 1 = 0 represents zerovelocity true/false.

V. CONCLUSION

A novel concept to use a compact low-power radar to improvethe accuracy of pedestrian inertial navigation was proposed and

implemented. This paper has described the design, prototyping,

and performance evaluation of the proposed radar. The exper-

imental results show that the proposed radar is promising for

sensing ZUPT and position, as well as velocity. Further hard-

ware development includes reducing size and power by inte-

grating all the components in the TRV box onto a small single

circuit board.

ACKNOWLEDGMENT

The U.S. Government is authorized to reproduce and dis-

tribute reprints for Governmental purposes notwithstandingany copyright notation thereon. The views and conclusions

contained herein are those of the authors and should not be

interpreted as necessarily representing the official policies or

endorsements, either expressed or implied, of the Air Force

Research Laboratory (AFRL), the Defense Advanced Research

Projects Agency (DARPA) or the U.S. Government.

This paper is approved for public release, distribution unlim-

ited.

REFERENCES

[1] E. Foxlin, Pedestrian tracking with shoe-mounted inertial sensors,IEEE Comput. Graph. Appl., vol. 25, no. 6, pp. 3846, Dec. 2005.

[2] L. Ojeda and J. Borenstein, Non-GPS navigation for security per-sonnel and first responders, J. Navigat., vol. 60, no. 3, pp. 391407,Sep. 2007.

8/7/2019 05565507

8/8


[3] R. Stirling, Developmentof a pedestrian navigation system using shoemounted sensors, Masters thesis, Dept. Mech. Eng., Univ. Alberta,Edmonton, AB, Canada, 2003.

[4] C. Fischer, K. Muthukrishnan, M. Hazas, and H. Gellersen, Ultra-sound-aided pedestrian dead reckoning for indoor navigation, in Proc.1st ACM Int. Mobile Entity Localization and Tracking in GPS-Less En-

vironments Workshop, New York, NY, 2008, pp. 3136.[5] C. Zhou, J. Downey, D. Stancil, and T. Mukherjee, A compact

positioning and velocity RF sensor for improved inertial navigation,in IEEE MTT-S Int. Microw. Symp., Boston, MA, Jun. 2009, pp.14211424.

[6] C. Li, J. Cummings, J. Lam, E. Graves, and W. Wu, Radar remotemonitoring of vital signs, IEEE Microw. Mag., vol. 10, no. 1, pp.4756, Jan. 2009.

[7] A. Mashhour, W. Domino, and N. Beamish, On the direct conversionreceiver-A tutorial, Microw. J., vol. 44, no. 6, pp. 114128, Jun. 2001.

[8] B. Razavi, Design considerations for direct conversion receivers, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 44,no. 6, pp. 428435, Jun. 1997.

[9] C. Zhou, J. Downey, D. Stancil, and T. Mukherjee, Compact shortrange RF motion sensor for improved inertial navigation, in Govern-ment Microcircuits Appl. Crit. Technol., Orlando, FL, Mar. 2009, pp.5356.

[10] I. Gupta and A. Ksienski, Effect of mutual coupling on the perfor-mance of adaptive arrays, IEEE Trans. Antennas Propag., vol. AP-31,

no. 5, pp. 785791, Sep. 1983.[11] M. Skolnik , Introduction to Radar Systems. New York: McGraw-

Hill, 1980.

Chenming Zhou (S05M08) was born in Jiangxi,China, in 1979. He received the B.S. degree inphysics from the Changsha University of Scienceand Technology, Changsha, China, in 2000, theM.S. degree in optics from the Beijing University of

Technology, Beijing, China, in 2003, and the Ph.Ddegree in electrical engineering from TennesseeTechnological University, Cookeville, in 2008.

He is currently a Project Research Scientist withthe Department of Electrical and Computer Engi-neering, Carnegie Mellon University, Pittsburgh,

PA. His general research interests include wireless communications, signalprocessing, and RF system design.

James Downey (S02) received the B.S.E.E degreefrom The University of Toledo, Toledo, OH, in2005, the M.S. degree in electrical and computerengineering from Carnegie Mellon University, Pitts-burgh, PA, in 2008, and is currently working towardthe Ph.D. degree at Carnegie Mellon University.

Mr. Downey is in the National Aeronautics andSpace Administration (NASA) Co-Op Program and

has been involved with optical measurements/di-agnostics and extra-vehicular activity (EVA)navigation with the Langley Research Center and

Glenn Research Center, respectively. His research interests include wirelesscommunications, antennas, navigation, radar, and optical measurements.

Daniel Stancil (S75M81SM91F04) receivedthe B.S. degree in electrical engineering fromTennessee Technological University, Cookeville, in1976, and the S.M., E.E., and Ph.D. degrees fromthe Massachusetts Institute of Technology (MIT),Cambridge, in 1978, 1979, and 1981, respectively.

In 2009, he returned to North Carolina State Uni-versity, Raleigh, as Head of the Electrical and Com-puter Engineering Department, where he is also cur-rently the Alcoa Distinguished Professor. From 1981to 1986, he was an Assistant Professor of electrical

and computer engineering with North Carolina State University. From 1986 to2009, he was an Associate Professor and then Professor of electrical and com-puter engineering with Carnegie Mellon University. His research interests in-clude wireless communications and applied electrodynamics.

Dr. Stancil is a past president of the IEEE Magnetics Society.

Tamal Mukherjee (S89M95) received the B.S.,M.S., and Ph.D. degrees in electrical and computerengineering from Carnegie Mellon University, Pitts-burgh, PA, in 1987, 1990, and 1995, respectively.His research interests include design techniquesand methodologies at the boundary of analog, RF,

MEMS, and microfluidic systems.He is currently a Professor with the Electrical

and Computer Engineering Department, CarnegieMellon University. His current research is focused onRF MEMS passive components and their insertion

into RF circuits for both enhanced performance and to achieve frequency re-configurability. He is also involved in the integration of MEMS inertial sensorswith RF sensors for localization applications in GPS-denied environments.

05565507

Documents