0 TA8b, Asilomar Object Tracking in a 2D UWB Sensor Network November 8th, 2004 Cheng Chang EECS Dept,UC Berkeley Joint work with Prof. Anant Sahai (funded by NSF)

1 TA8b, Asilomar 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

2 TA8b, Asilomar 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

3 TA8b, Asilomar 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

4 TA8b, Asilomar 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.

5 TA8b, Asilomar Multipath Measurements R T

6 TA8b, Asilomar Single Tx, Single Rx A single multipath distance is not enough to locate an object

7 TA8b, Asilomar A Strict Motion Model In principle, can solve for position within a 4-fold symmetry Constant velocity model parameterized as (x 0,y 0,x N,y N ), where (x 0, y 0 ), (x N, y N ) are the starting and ending positions of the object.

8 TA8b, Asilomar CR Bound Huge CR bounds  bad estimation performance

9 TA8b, Asilomar Why is the CRB bad? Fragile dependence on the constant velocity assumption All three motions have the same multi-path profile

10 TA8b, Asilomar Multiple Tx, Single Rx A 3 transmitter 1 receiver sensor network Position of the object can be determined by using ellipse laceration.

11 TA8b, Asilomar 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.

12 TA8b, Asilomar CRB for Multiple Tx, Single Rx An N transmitter 1 receiver sensor network Normalized CR bound Constant total transmit power

13 TA8b, Asilomar CRB for Multiple Tx, Single Rx N=4 N=6 N=10 N=20

14 TA8b, Asilomar CRB for Multiple Tx, Single Rx (faraway region) N=10, it appears that estimates are bad outside of the sensor region

15 TA8b, Asilomar Look in Polar Coordinates

16 TA8b, Asilomar Analysis for Multiple Tx, Multiple Rx Theoretical VS simulation CR bound ~1/NM Estimation performance improves with total energy collected by receivers

17 TA8b, Asilomar Dense Network Asymptotics N Tx, M RxN Tx, Single Rx Inside the network Outside L: distance to the network r: size of the SN Outside Polar coordinates

18 TA8b, Asilomar A Semi-linear Estimation Scheme Multi-path distance : –(x,y) unknown position of the object –d ij : multi-path distance from Tx i to Rx j, (i=1,2..M; j=1,2…N) –(a i,b i ),(u j,v j ) 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 (2+M+N) matrix, v =(x,y, l 1 T, l 2 T … l M T,l 1 R, l 2 R. … l N R. ) T v=(A T A) -1 A T b The scheme is order optimal Is the distance between object and ith Tx Is the distance between object and jth Rx

19 TA8b, Asilomar 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

20 TA8b, Asilomar A Heuristic Algorithm Hough Transform-like algorithm 1.Discretize the search region 2.Use measured channels to assign scores to grid points. Searching for high scores. 3.Read correspondences out from candidate locations. 4.Fine estimation scheme for single object.

21 TA8b, Asilomar Simulation Result A 7 transmitter 7 receiver sensor network with 5 objects Score function

22 TA8b, Asilomar 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, you’d rather have a smaller-denser sensor network

23 TA8b, Asilomar 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

24 TA8b, Asilomar 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