Performance analysis of a distributed Robbins-Monro algorithm for sensor networks

This paper investigates the rate of convergence of a distributed Robbins-Monro algorithm for sensor networks. The algorithm under study consists of two steps: a local Robbins-Monro step at each sensor and a gossip step that drives the network to a consensus. Under verifiable sufficient conditions, we give an explicit rate of convergence for this algorithm and provide a conditional Central Limit Theorem. Our results are applied to distributed source localization.