1. 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. 2 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

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

4. 4 4 Research Issues Networking Issues ● Initialization, architecture, protocols, placement, fault-tolerance, security Signal Processing Issues ● Detection, estimation, tracking, recognition, compression, fusion, collaboration System Constraints ● Bandwidth, energy, time

5. 5 5 Radar Networks for Homeland Security [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

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

7. 7 7 Typical Signal Processing Scenario Addressed

8. 8 8 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

9. 9 9 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.

10. 10 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 [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.

11. 11 Background - Fisher Information and PCRLB

12. 12 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. [6] Zuo, Niu, and Varshney, IEEE T-SP, 2011.

13. 13 Conditional Posterior Cramer-Rao lower Bound

14. 14 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. [7] Masazade, Niu, Varshney, and Keskinoz, IEEE T-SP, 2010

15. 15 Complexity of the MI and C-PCRLB

16. 16 Sensor Selection for Static Source Localization M=4 bits per sensor observation 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. [7] Masazade, Niu, Varshney, and Keskinoz, IEEE T-SP, 2010

17. 17 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 [8] Zuo, Niu, and Varshney, ICASSP, 2007. [9] Zuo, Niu, and Varshney, ICASSP, 2008. [10] Hernandez, Kirubarajan, and Bar-Shalom, IEEE T-AES, 2004.

18. 18 Numerical Results: Object Trajectories

19. 19 Numerical Results: RMSEs

20. 20 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

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

24. 24 Differentiate the joint CDF to get the joint PDF N marginals (E.g., from N sensors) Uniform random variables! Copula density Product density Independence Copula Theory

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

27. 27 Copula-based Hypothesis Testing 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 GLR under independence Dependence term

28. 28 Results: Seismic-acoustic Fusion

29. 29 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