Convergence of a distributed parameter estimator for sensor networks with local averaging of the estimates

The paper addresses the convergence of a decentralized Robbins-Monro algorithm for networks of agents. This algorithm combines local stochastic approximation steps for finding the root of an objective function, and a gossip step for consensus seeking between agents. We provide verifiable sufficient conditions on the stochastic approximation procedure and on the network so that the decentralized Robbins-Monro algorithm converges to a consensus. We also prove that the limit points of the algorithm correspond to the roots of the objective function. We apply our results to Maximum Likelihood estimation in sensor networks.