Distributed Detection over Noisy Networks: Large Deviations Analysis

Abstract

We study the large deviations performance of consensus+innovations distributed detection over noisy networks, where sensors at a time step k cooperate with immediate neighbors (consensus) and assimilate their new observations (innovation.) We show that, even under noisy communication, \emph{all sensors} can achieve exponential decay e^{-k C_{\mathrm{dis}}} of the detection error probability, even when certain (or most) sensors cannot detect the event of interest in isolation. We achieve this by designing a single time scale stochastic approximation type distributed detector with the optimal weight sequence {α_k}, by which sensors weigh their neighbors' messages. The optimal design of {α_k} balances the opposing effects of communication noise and information flow from neighbors: larger, slowly decaying α_k improves information flow but injects more communication noise. Further, we quantify the best achievable C_{\mathrm{dis}} as a function of the sensing signal and noise, communication noise, and network connectivity. Finally, we find a threshold on the communication noise power below which a sensor that can detect the event in isolation still improves its detection by cooperation through noisy links.

30 pages, journal, submitted August 2nd, 2011

References in corpus (5)

• Sensor Networks with Random Links: Topology Design for Distributed Consensus
• Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs
• Diffusion Adaptation over Networks under Imperfect Information Exchange and Non-stationary Data
• Weight Optimization for Consensus Algorithms with Correlated Switching Topology
• Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations

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• Distributed Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics
• Statistical Hypothesis Testing Based on Machine Learning: Large Deviations Analysis
• Distributed Learning with Adversarial Agents Under Relaxed Network Condition
• Distributed Bayesian Quickest Change Detection in Sensor Networks via Two-layer Large Deviation Analysis
• Distributed Detection in Ad Hoc Networks Through Quantized Consensus