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arXiv · 1108.1410

Distributed Detection over Noisy Networks: Large Deviations Analysis

Dusan Jakovetic·Jose M. F. Moura·Joao Xavier
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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.

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Dusan Jakovetic, Jose M. F. Moura, Joao Xavier. 2011-08-05. Distributed Detection over Noisy Networks: Large Deviations Analysis. https://doi.org/10.1109/tsp.2012.2197395

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