Decentralized detection via running consensus

Consensus by sensor gossip, which ensures information retrieval from any subset of sensors at an arbitrary instant of time, is a popular paradigm for modern sensor networks designed for inference purposes. In realistic applications, the network continuously senses the surrounding environment, while consensus among its nodes is simultaneously enforced. The basic consensus equation is coherently modified allowing the sensor state update to include both the consensus contribution of neighboring nodes and new measurements. This new paradigm is often referred as running consensus. We review the state-of-the-art of running consensus techniques and discuss their applications with special emphasis to detection problems. The running consensus, when compared with the ideal centralized detection statistic, is affected by an error term that, under suitable conditions, can be negligible. We study such conditions exploiting the theory of locally optimum statistics. We prove the asymptotic equivalence of the running consensus with the ideal centralized system, in terms of detection capabilities. Specifically, such asymptotic optimality is demonstrated for two cases: the fixed sample size (FSS) test and the sequential test.