Object Tracking in a 2D UWB Sensor Network

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

2. 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 TA8b, Asilomar 2004

3. 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 TA8b, Asilomar 2004

4. 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 TA8b, Asilomar 2004

5. 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. TA8b, Asilomar 2004

6. T R Multipath Measurements TA8b, Asilomar 2004

7. Single Tx, Single Rx A single multipath distance is not enough to locate an object TA8b, Asilomar 2004

8. 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 TA8b, Asilomar 2004

9. CR Bound Huge CR bounds  bad estimation performance TA8b, Asilomar 2004

10. Why is the CRB bad? All three motions have the same multi-path profile Fragile dependence on the constant velocity assumption TA8b, Asilomar 2004

11. Multiple Tx, Single Rx • A 3 transmitter 1 receiver sensor network • Position of the object can be determined by using ellipse laceration. TA8b, Asilomar 2004

12. Multiple Tx, Single Rx • Estimation Bounds • The Fisher Information matrix Jis 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. TA8b, Asilomar 2004

13. CRB for Multiple Tx, Single Rx An N transmitter 1 receiver sensor network Normalized CR bound Constant total transmit power TA8b, Asilomar 2004

14. CRB for Multiple Tx, Single Rx N=4 N=10 N=6 N=20 TA8b, Asilomar 2004

15. CRB for Multiple Tx, Single Rx (faraway region) N=10, it appears that estimates are bad outside of the sensor region TA8b, Asilomar 2004

16. Look in Polar Coordinates TA8b, Asilomar 2004

17. Analysis for Multiple Tx, Multiple Rx Theoretical VS simulation CR bound ~1/NM Estimation performance improves with total energy collected by receivers TA8b, Asilomar 2004

18. Dense Network Asymptotics TA8b, Asilomar 2004

19. Multi-path distance : (x,y) unknown position of the object dij : multi-path distance from Tx i to Rx j , (i=1,2..M; j=1,2…N) (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 (2+M+N) matrix, v =(x,y, l1T, l2T … lMT,l1R, l2R. … lNR.)Tv=(ATA) -1ATb The scheme is order optimal A Semi-linear Estimation Scheme Is the distance between object and ith Tx Is the distance between object and jth Rx TA8b, Asilomar 2004

20. 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 TA8b, Asilomar 2004

21. 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. TA8b, Asilomar 2004

22. Simulation Result • A 7 transmitter 7 receiver sensor network with 5objects Score function TA8b, Asilomar 2004

23. 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 TA8b, Asilomar 2004

24. 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 TA8b, Asilomar 2004

25. 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 TA8b, Asilomar 2004