1. 0 TA8b, Asilomar 20040 Object Tracking in a 2D UWB Sensor Network November 8th, 2004 Cheng Chang EECS Dept,UC Berkeley cchang@eecs.berkeley.edu Joint work with Prof. Anant Sahai (funded by NSF)

2. 1 TA8b, Asilomar 20041 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

3. 2 TA8b, Asilomar 20042 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

4. 3 TA8b, Asilomar 20043 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

5. 4 TA8b, Asilomar 20044 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.

6. 5 TA8b, Asilomar 20045 Multipath Measurements R T

7. 6 TA8b, Asilomar 20046 Single Tx, Single Rx A single multipath distance is not enough to locate an object

8. 7 TA8b, Asilomar 20047 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.

9. 8 TA8b, Asilomar 20048 CR Bound Huge CR bounds  bad estimation performance

10. 9 TA8b, Asilomar 20049 Why is the CRB bad? Fragile dependence on the constant velocity assumption All three motions have the same multi-path profile

11. 10 TA8b, Asilomar 200410 Multiple Tx, Single Rx A 3 transmitter 1 receiver sensor network Position of the object can be determined by using ellipse laceration.

12. 11 TA8b, Asilomar 200411 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.

13. 12 TA8b, Asilomar 200412 CRB for Multiple Tx, Single Rx An N transmitter 1 receiver sensor network Normalized CR bound Constant total transmit power

14. 13 TA8b, Asilomar 200413 CRB for Multiple Tx, Single Rx N=4 N=6 N=10 N=20

15. 14 TA8b, Asilomar 200414 CRB for Multiple Tx, Single Rx (faraway region) N=10, it appears that estimates are bad outside of the sensor region

16. 15 TA8b, Asilomar 200415 Look in Polar Coordinates

17. 16 TA8b, Asilomar 200416 Analysis for Multiple Tx, Multiple Rx Theoretical VS simulation CR bound ~1/NM Estimation performance improves with total energy collected by receivers

18. 17 TA8b, Asilomar 200417 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

19. 18 TA8b, Asilomar 200418 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

20. 19 TA8b, Asilomar 200419 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

21. 20 TA8b, Asilomar 200420 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.

22. 21 TA8b, Asilomar 200421 Simulation Result A 7 transmitter 7 receiver sensor network with 5 objects Score function

23. 22 TA8b, Asilomar 200422 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

24. 23 TA8b, Asilomar 200423 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

25. 24 TA8b, Asilomar 200424 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