Distributed Detection over Random Networks: Large Deviations Analysis

Abstract: We show by large deviations theory that the performance of running consensus is asymptotically equivalent to the performance of the (asymptotically) optimal centralized detector. Running consensus is a stochastic approximation type algorithm for distributed detection in sensor networks, recently proposed. At each time step, the state at each sensor is updated by a local averaging of its own state and the states of its neighbors (consensus) and by accounting for the new observations (innovation). We assume Gaussian, spatially correlated observations, and we allow for the underlying network to be randomly varying. This paper shows through large deviations that the Bayes probability of detection error, for the distributed detector, decays at the best achievable rate, namely, the Chernoff information rate. Numerical examples illustrate the behavior of the distributed detector for finite number of observations.