Transcript Slide 1

Signal Processing and Information
Fusion with Networked Sensors
Pramod K. Varshney
Electrical Engineering and Computer Science Dept.
Syracuse University
[email protected]
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
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Sensor Networks and Information Fusion
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Signal processing hot topics!
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Information collection from distributed heterogeneous sensors
Radar sensor networks
Bi-static/Multi-static/MIMO radars not the focus here
Inference in the presence of resource constraints
Fusing heterogeneous, correlated data
Conclusion
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Wireless Sensor Networks
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WSNs integrate a large number of low cost computationallylimited processors.
These processors have flexible interfaces allowing various
sensors to be networked.
Fusion Center
Sensor and
Local processor
Ad Hoc Network Topology
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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”
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www.math.colostate.edu/~estep/cims/imaging/talks/Chan
drasekar.ppt
Typical Signal Processing Scenario Addressed
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Signal Processing Hot Topics!
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Inference driven management in sensor networks
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Sensor selection for source localization
Sensor selection for object tracking
Bandwidth management for object tracking, etc
Heterogeneous data fusion in sensor networks
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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
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State of the art sensor management approaches are based on
posterior entropy or mutual information [3-5].
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Information theoretic measures suffers from
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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]
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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 ?
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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.
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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
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Problem Formulation [7]:
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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
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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
•The computational
complexity of MI based
sensor selection increases
exponentially with the
number of activated
sensors per iteration.
M=4 bits per sensor observation
[7] Masazade, Niu, Varshney, and Keskinoz, IEEE T-SP, 2010
•The computational
complexity of PCRLB
based sensor selection
increases linearly with
the number of activated
sensors per iteration.
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Sensor Selection for Object Tracking
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Problem Formulation [8-9]:
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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:
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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
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Statistical dependence is either ignored or not adequately
considered
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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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Copula Theory
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Differentiate the joint CDF to get the joint PDF
Product density
N marginals
(E.g., from N sensors)
Independence
Uniform random variables!
Copula density
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Bivariate density: Normal and Gamma Marginals
Gumbel Copula  = 2
Bivariate Normal,  = 0.5
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Summary of Copula Functions
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Copulas are typically defined as a CDF
Elliptical copulas: derived from multivariate distributions
Gaussian copula
t-copula
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Archimedean Copulas
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Copula-based Hypothesis Testing
GLR under independence
Dependence term
Copula based test-statistic decouples marginal and
dependency information
 Information theoretic analysis & detailed formulation of
copula-based signal inference*
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[11] Iyengar, Varshney, and Damarla, IEEE T-SP, 2011
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Results: Seismic-acoustic Fusion
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Ongoing and Future Work
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Inference driven management in sensor networks
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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
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Fusion of multimodal sensors and homogeneous sensors
Multi-algorithm Fusion, e.g., multi-biometrics
Multi-classifier Fusion – Fusing different classifiers
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