Signal Processing and Information Fusion with Networked Sensors

1. Signal Processing and Information Fusion with Networked Sensors Pramod K. Varshney Electrical Engineering and Computer Science Dept. Syracuse University varshney@syr.edu This research was supported by ARO under Grant W911NF-09-1-0244 and U.S. Air Force Office of Scientific Research (AFOSR) under Grant FA9550-10-1-0263

2. Overview • Sensor Networks and Information Fusion • Information collection from distributed heterogeneous sensors • Radar sensor networks • Bi-static/Multi-static/MIMO radars not the focus here • Signal processing hot topics! • Inference in the presence of resource constraints • Fusing heterogeneous, correlated data • Conclusion 2

3. Wireless Sensor Networks • WSNs integrate a large number of low cost computationally-limited processors. • These processors have flexible interfaces allowing various sensors to be networked. Fusion Center Sensor and Local processor Ad Hoc Network Topology 3

4. Radar Networks for Homeland Security 5 [1] Nohara, T.J.; Weber, P.; Jones, G.; Ukrainec, A.; Premji, A.; , "Affordable High-Performance Radar Networks for Homeland Security Applications," Radar Conference, 2008. RADAR '08. IEEE , pp.1-6, 26-30 May 2008

5. Measurement at each radar node Networked retrieval Networked radar - Precipitation imaging [2] V.Chandrasekar, “Ground-based and Space-based Radar Precipitation Imaging” www.math.colostate.edu/~estep/cims/imaging/talks/Chandrasekar.ppt 6

6. Typical Signal Processing Scenario Addressed 7

7. Signal Processing Hot Topics! • Inference driven management in sensor networks • Sensor selection for source localization • Sensor selection for object tracking • Bandwidth management for object tracking, etc • Heterogeneous data fusion in sensor networks • Copula based framework 8

8. Inference Driven Management in Sensor Networks Determining the optimal way to manage system resources and task a group of sensors to collect measurements for statistical inference. 9

9. Motivation • State of the art sensor management approaches are based on posterior entropy or mutual information [3-5]. • Information theoretic measures suffers from • Complexity exponential in the number of sensors to be managed • Lack of direct link to estimation performance • Adaptive sensor management based on the fundamentally new recursive conditional PCRLB on MSE [6] • Complexity linear in number of sensors when sensor noises are independent • Provides a lower bound on MSE for any nonlinear Bayesian filter 10 [3] Zhao, Shin, and Reich, IEEE SPM, 2002. [4] Kreucher, Hero, Kastella, and Morelande, Proc. of IEEE, 2007. [5] Williams, Fisher, and Willsky, IEEE T-SP, 2007. [6] Zuo, Niu, and Varshney, IEEE T-SP, 2011.

10. Background - Fisher Information and PCRLB

11. Why Conditional PCRLB ? • Unconditional PCRLB: FIM derived by taking expectation with respect to the joint distribution of the measurements and the object states, which makes the PCRLB an off-line bound. • Independent of any specific realization of the state track, so it can not reflect the online state estimation performance for a particular realization very faithfully. • Solution: the conditional PCRLB [6] is dependent on the past observed data and hence implicitly dependent on the state track up to the current time. Hence an on-line bound. 12 [6] Zuo, Niu, and Varshney, IEEE T-SP, 2011.

12. Conditional Posterior Cramer-Rao lower Bound 13

13. Sensor Selection for Source Localization • Problem Formulation [7]: • Signal amplitudes follow an Isotropic power attenuation model. • Noisy signal is quantized locally and transmitted to a FC. • Instead of requesting data from all the sensors, fusion center iteratively selects sensors for source localization • First, a small number of anchor sensors send their data to the fusion center to obtain a coarse location estimate. • Then, at each step a few (A) non-anchor sensors are activated to send their data to the fusion center to refine the location estimate iteratively. 14 [7] Masazade, Niu, Varshney, and Keskinoz, IEEE T-SP, 2010

14. Complexity of the MI and C-PCRLB 15

15. Sensor Selection for Static Source Localization • The computational complexity of MI based sensor selection increases exponentially with the number of activated sensors per iteration. • The computational complexity of PCRLB based sensor selection • increases linearly with the number of activated sensors per iteration. M=4 bits per sensor observation 16 [7] Masazade, Niu, Varshney, and Keskinoz, IEEE T-SP, 2010

16. Sensor Selection for Object Tracking • Problem Formulation [8-9]: • 30 bearing-only sensors randomly deployed in a surveillance area • An object moves in the field according to white noise acceleration model. • At each time step, two sensors are activated to transmit bearing readings of the object to the fusion center, to minimize the C-PCRLB • Comparison with other approaches: • Information-driven approach based on maximum MI • PCRLB with renewal strategy [10] • Nearest neighbor approach 17 [8] Zuo, Niu, and Varshney, ICASSP, 2007. [9] Zuo, Niu, and Varshney, ICASSP, 2008. [10] Hernandez, Kirubarajan, and Bar-Shalom, IEEE T-AES, 2004.

17. Numerical Results: Object Trajectories 18

18. Numerical Results: RMSEs 19

19. Fusion of Heterogeneous Signals • Statistical dependence is either ignored or not adequately considered • How do we characterize dependence? • How do we include it in the distributed inference algorithms? • We develop a copula theory based approach for a variety of distributed inference problems 20

22. Copula Theory 23 Copulas are functions that couple marginals to form a joint distribution Sklar’s Theorem is a key result – existence theorem

23. Copula Theory Nmarginals (E.g., from N sensors) Product density Independence Uniform random variables! Copula density Differentiate the joint CDF to get the joint PDF

24. 25

25. Summary of Copula Functions • Copulas are typically defined as a CDF • Elliptical copulas: derived from multivariate distributions • Archimedean Copulas Gaussian copula t-copula 26

26. Copula-based Hypothesis Testing GLR under independence Dependence term 27 Copula based test-statistic decouples marginal and dependency information Information theoretic analysis & detailed formulation of copula-based signal inference* [11] Iyengar, Varshney, and Damarla, IEEE T-SP, 2011

27. Results: Seismic-acoustic Fusion 28

28. Ongoing and Future Work • Inference driven management in sensor networks • Relationship between information theoretic and estimation theoretic measures • Sensor management by optimizing multiple objectives • Non-myopic (multi-step-ahead) sensor management • Channel-aware sensor/resource management • Heterogeneous data fusion in sensor networks • Fusion of multimodal sensors and homogeneous sensors • Multi-algorithm Fusion, e.g., multi-biometrics • Multi-classifier Fusion – Fusing different classifiers 29