Distributed Detection via Gaussian Running Consensus: Large Deviations Asymptotic Analysis

We study, by large deviations analysis, the asymptotic performance of Gaussian running consensus distributed detection over random networks; in other words, we determine the exponential decay rate of the detection error probability. With running consensus, at each time step, each sensor averages its decision variable with the neighbors´ decision variables and accounts on-the-fly for its new observation. We show that: 1) when the rate of network information flow (the speed of averaging) is above a threshold, then Gaussian running consensus is asymptotically equivalent to the optimal centralized detector, i.e., the exponential decay rate of the error probability for running consensus equals the Chernoff information; and 2) when the rate of information flow is below a threshold, running consensus achieves only a fraction of the Chernoff information rate. We quantify this achievable rate as a function of the network rate of information flow. Simulation examples demonstrate our theoretical findings on the behavior of running consensus detection over random networks.