Heping Song , Tong Liu, Xiaomu Luo and Guoli Wang
description
Transcript of Heping Song , Tong Liu, Xiaomu Luo and Guoli Wang
2011-7-28 P. 1/30
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!