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Signal Processing and Information Fusion with Networked Sensors

Pramod K. VarshneyElectrical Engineering and Computer Science Dept. Syracuse Universityvarshney@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

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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

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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 andLocal processor

Wireless Sensor Networks

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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

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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/Chandrasekar.ppt

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Typical Signal Processing Scenario Addressed

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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

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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.

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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.

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Background - Fisher Information and PCRLB

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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.

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Conditional Posterior Cramer-Rao lower Bound

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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

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Complexity of the MI and C-PCRLB

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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

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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.

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Numerical Results: Object Trajectories

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Numerical Results: RMSEs

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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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Copula Theory Copulas are functions that couple marginals to form a

joint distribution Sklar’s Theorem is a key result – existence theorem

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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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Bivariate Normal, = 0.5

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

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Bivariate density: Normal and Gamma MarginalsGumbel Copula = 2

-2 -1.5 -1 -0.5 0 0.5 1 1.5

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Summary of Copula Functions Copulas are typically defined as a CDF Elliptical copulas: derived from multivariate distributions

Archimedean Copulas

Gaussian copulat-copula

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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 independenceDependence term

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Results: Seismic-acoustic Fusion

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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