Template for MCMA Poster Slides

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Object Tracking in a 2D UWB Sensor Network
November 8th, 2004 Cheng Chang EECS Dept ,UC
Berkeley cchang_at_eecs.berkeley.edu Joint work
with Prof. Anant Sahai (funded by NSF)
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Outline

• Information from channel estimates
• Single object tracking
• Estimation bounds Cramer Rao lower bound
• Asymptotic analysis (number of sensors ? )
• Multiple objects
• A heuristic algorithm for multiple transmitter
  multiple receiver
• Effects of network scaling

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Assumptions

• Synchronized sensor-network with communication
  capability
• Critical for multiple receiver network
• Good synchronized clocks
• Transmitter/Receivers with known positions
• Channel response with high resolution (UWB)
• High speed A/D converter GHz
• Can be extracted from data packets
• Slowly changing environment

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Side effect of communication

• Pairwise impulse responses
• Training data
• Successful data packets
• Our abstract model
• Good SNR after processing
• Paths corresponds to bounces off objects

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Multipath Length Extraction

• Signal Model Received signal background
  response bounces from new/moving objects
• Background response is considered known
• High SNR sub-sample precision on path
  resolution
• Noise Model Noise in channel estimation induces
  noise in path length estimation, modeled as AWGN
  with known variances.

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Multipath Measurements
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Single Tx, Single Rx

• A single multipath distance is not enough to
  locate an object

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A Strict Motion Model

• Constant velocity model
• parameterized as (x0,y0,xN,yN), where (x0, y0),
  (xN, yN) are the starting and ending positions of
  the object.

• In principle, can solve for position within a
• 4-fold symmetry

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CR Bound
Huge CR bounds ? bad estimation performance
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Why is the CRB bad?
All three motions have the same multi-path
profile
Fragile dependence on the constant velocity
assumption
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Multiple Tx, Single Rx

• A 3 transmitter 1 receiver sensor network

• Position of the object can be determined by
• using ellipse laceration.

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Multiple Tx, Single Rx

• Estimation Bounds
• The Fisher Information matrix J is a 2 by 2
  matrix
• Cramer-Rao bound for (x,y) is

• An N receiver 1 transmitter sensor network
• has the same Fisher Information Matrix.

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CRB for Multiple Tx, Single Rx
An N transmitter 1 receiver sensor network
Normalized CR bound Constant total transmit power
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CRB for Multiple Tx, Single Rx
N4
N10
N6
N20
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CRB for Multiple Tx, Single Rx (faraway region)
N10, it appears that estimates are bad outside
of the sensor region
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Look in Polar Coordinates
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Analysis for Multiple Tx, Multiple Rx
Theoretical VS simulation CR bound 1/NM
Estimation performance improves with total energy
collected by receivers
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Dense Network Asymptotics
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A Semi-linear Estimation Scheme

• Multi-path distance
• (x,y) unknown position of the object
• dij multi-path distance from Tx i to Rx j ,
  (i1,2..M j1,2N)
• (ai,bi),(uj,vj) are known positions of the
  transmitter i and receiver j
• Rewrite (1) as
• MN multi-path distance measures, 2MN linear
  equations as (2.1) or (2.2)
• A v b Where A is an 2MN X (2MN)
  matrix, v (x,y, l1T, l2T lMT,l1R, l2R.
  lNR.)T v(ATA) -1ATb
• The scheme is order optimal

Is the distance between object and ith Tx
Is the distance between object and jth Rx
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Multiple Objects

• L objects of interest in environment
• More pair-wise impulse responses
• Correspondence issue must identify paths to same
  object
• (L!)NM-1 possible combinations
• Exhaustive search for all possibilities is
  unrealistic

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A Heuristic Algorithm

• Hough Transform-like algorithm
• Discretize the search region
• Use measured channels to assign scores to grid
  points. Searching for high scores.
• Read correspondences out from candidate
  locations.
• Fine estimation scheme for single object.

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Simulation Result
A 7 transmitter 7 receiver sensor network with 5
objects
Score function
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Network Scaling

• Noise variance of the multi-path length
  extraction is dependent on the length of the
  multi-path
• Sensor-network 1 is scaled up by factor c from
  sensor-network 2.
• With same total power, youd rather have a
  smaller-denser sensor network

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Conclusions

• Object can not be tracked in a Single Tx Single
  Rx network (high Cramer Rao bound)
• The Cramer Rao bounds are reasonably low for
  MTSR/ MTMR network
• The 2-step estimation scheme works well for
  multiple object tracking

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Future Work

• Low SNR Joint channel and position estimation
• Move beyond specular reflection model
• Exploit for communication
• Inverse problem
• Boost the communication capacity
• Channel prediction under some reasonable motion
  model