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Heping Song, Tong Liu, Xiaomu Luo and Guoli

Wang

Feedback based Sparse Recovery

for Motion Tracking

in RF Sensor Networks

IEEE Inter. Conf. on Networking, Architecture, and Storage (NAS 2011)

July 28-30, 2011, Dalian, China

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Outline

Experiments

3

Discussions

Sparse Recovery

Introduction

Motivation

Linear Model

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An image is a grid of pixels

Matrix = a grid of pixels

color by number

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Tomography

Tomo- means “a slice/section/part” in Greek

Wikipedia

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Magic Square

4 9 2

3 5 7

8 1 6

1515

151

515

15

15

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RF Sensor Networks

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The Network Layout

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Radio Tomography Imaging

x1 x4 x7

x2 x5 x8

x3 x6 x9

y6

y5

y2 y3y1

y4

y xInverse problem

Weighted Sum

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Linear Model

y Ax n

,

: measured losses (dB) vs. empty

: discretized loss field (dB/pixel)

: weights/shadowing loss added to

link caused by motion in pixel

: noise

i j

y

x

A

i j

n

Model: Assume shadowing loss is linear combination of motion occurring in each pixel

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Elliptical Weight Model

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Video cameras. Don’t work in dark, through smoke or walls. Privacy concerns.

Thermal imagers. Limited by walls. High cost.

Motion detectors. Also limited by walls. High false alarms.

Ultra wideband (UWB) radar. High cost.

Received signal strength (RSS) in WSN

Device-free Localization (DFL)

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Track image max x/ Kalman filter

The sparse nature of location finding

Directly track the location of moving targets

Motivation

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Sparse Recovery

y Ax

1

Measure , assume known . Estimate .

-minimization : BP etc.

Greedy algorithm: , CoSaMP, SP eOMP tc.

y A x

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Greedy Sparse Recovery

Support Detection

Signal Estimation

A, y x

I Iy A x

† ;

0I I

I

x A y

x

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Support Detection Strategy

Select atoms of measurement matrix A to generate y

Determine active atoms in sparse representation of x

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Orthogonal Matching Pursuit (OMP)

1: arg max ,Tt

jOMP A r r y Ax

1

†

1.support detection : { }

2.signal estimation : ; 0

t t

I I I

I I j

x A y x

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Demo - OMP(1)

10 20 30 40 50 60

-1

-0.5

0

0.5

1

Sparsity= 4, detected(total= 1, good= 1, bad= 0, miss= 3), RelErr=8.39e-001

true signaltrue nonzero

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Demo - OMP(2)

10 20 30 40 50 60

-1

-0.5

0

0.5

1

Sparsity= 4, detected(total= 2, good= 2, bad= 0, miss= 2), RelErr=6.08e-001

true signaltrue nonzero

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Demo - OMP(3)

10 20 30 40 50 60

-1

-0.5

0

0.5

1

Sparsity= 4, detected(total= 3, good= 3, bad= 0, miss= 1), RelErr=3.34e-001

true signaltrue nonzero

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Demo - OMP(4)

10 20 30 40 50 60

-1

-0.5

0

0.5

1

Sparsity= 4, detected(total= 4, good= 4, bad= 0, miss= 0), RelErr=6.19e-016

true signaltrue nonzero

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Compressed Measurements

Weight matrix --overcomplete dictionary

Feedback information

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Heuristic Selection via Feedback Info.

xi

previous localization

block neighborhood

crossed links

compressed measurements

ix

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Feedback Structure

Predicted support

The locations of the previous frame

Recovered support

Sparse recovery

Next frame

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Experiments-1 resolution 6x6

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Experiments-2 resolution 13x13

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Experiments-3 resolution 27x27

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Experiments-4 compressed meas.

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Experiments-5 compressed meas.

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Experiments-6 compressed meas.

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Discussions

Thank Thank You!You!