Distributed Quickest Detection in Sensor Networks via Two-Layer Large Deviation Analysis

Abstract

We propose a distributed Bayesian quickest detection algorithm for sensor networks, based on a random gossip inter-sensor communication structure. Without a control or fusion center, each sensor executes its local change detection procedure in a parallel and distributed fashion, interacting with its neighboring sensors via random inter-sensor communications to propagate information. By modeling the information propagation dynamics in the network as a Markov process, a two-layer large deviation analysis is presented to analyze the performance of the proposed algorithm. The first-layer analysis shows that the relation between the probability of false alarm and the conditional averaged detection delay satisfies the large deviation principle, where the distributed Kullback–Leibler information number is established as a crucial factor. The second-layer analysis studies the probability that not all observations are available at one sensor. It shows that this probability decays exponentially fast to zero as the averaged rounds of communication increases. The large deviation upper and lower bounds for the converge rate are then derived. Finally, we show that the performance of the distributed algorithm converges exponentially fast to that of the centralized optimal one.