Stepsize Sequence Design for Distributed Average Consensus

Starting from local observations, iterative consensus algorithms attempt to drive a sensor network to a common estimate in a decentralized, incremental manner. When additive noise perturbs the sensor exchanges, a decreasing stepsize guarantees convergence under certain conditions, although the design of such stepsize sequence for fastest convergence is an unsettled issue. We present a greedy approach to stepsize sequence design, which minimizes the mean squared error at each iteration. This design requires knowledge of the network topology; in order to overcome this drawback, a modified design based only on average descriptors of the network is also developed.