Decentralized asymptotic detection by running consensus

A Wireless Sensor Network is engaged in a binary detection task and the operational modality is that known as running consensus: Each node continuously collects data and simultaneously exchanges informations with its neighbors, with the final aim of reaching agreement about a common detection statistic. This paper exploits an appropriate framework for investigating the detection performance of the system, in the limit of large sample sizes, under both the Neyman-Pearson and the sequential detection paradigms. The main result is that the running consensus detector is asymptotically optimal, in the sense that its performance approaches that of an ideal centralized entity to which all the data globally sensed by the network are made available.