Distributed estimation in the presence of correlated noises

We propose a method for distributed sequential estimation in the presence of correlated noises. At each time slot, a node exchanges information with its neighbors and then updates the estimate by using the received information from its neighbors and its local observation. It is assumed that the noises have the Markov property with respect to the network topology. A doubly stochastic matrix for combining information from the nodes is employed to average the sufficient statistics over the network. We show that the performance of the proposed method converges to that of the centralized optimal estimator as the iterations go on. Therefore, our algorithm approaches the Cramér-Rao bound asymptotically.