Distributed Detection via Gaussian Running Consensus: Large Deviations Asymptotic Analysis

We study, by large deviations analysis, the asymptotic performance of Gaussian running consensus distributed detection over random networks; in other words, we determine the exponential decay rate of the detection error probability. With running consensus, at each time step, each sensor averages its...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2011-09, Vol.59 (9), p.4381-4396
Main Authors: Bajovic, D., Jakovetic, D., Xavier, J., Sinopoli, B., Moura, J. M. F.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic properties
Chernoff information
Decay rate
Detection, estimation, filtering, equalization, prediction
Detectors
Deviation
distributed detection
Error detection
Error probability
Estimation
Exact sciences and technology
Gaussian
Information flow
Information, signal and communications theory
large deviations
Networks
Noise
random network
Robot sensing systems
Running
running consensus
Signal and communications theory
Signal, noise
Studies
Telecommunications and information theory
Testing
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Summary:We study, by large deviations analysis, the asymptotic performance of Gaussian running consensus distributed detection over random networks; in other words, we determine the exponential decay rate of the detection error probability. With running consensus, at each time step, each sensor averages its decision variable with the neighbors' decision variables and accounts on-the-fly for its new observation. We show that: 1) when the rate of network information flow (the speed of averaging) is above a threshold, then Gaussian running consensus is asymptotically equivalent to the optimal centralized detector, i.e., the exponential decay rate of the error probability for running consensus equals the Chernoff information; and 2) when the rate of information flow is below a threshold, running consensus achieves only a fraction of the Chernoff information rate. We quantify this achievable rate as a function of the network rate of information flow. Simulation examples demonstrate our theoretical findings on the behavior of running consensus detection over random networks.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2157147