A BP-like Distributed Algorithm for Weighted Average Consensus

A novel distributed algorithm designed for weighted average consensus is presented. This algorithm is developed based on the well-known Belief Propagation (BP) algorithm for statistical learning. For a connected network without loops, the algorithm will converge in finite number of iteration and produces a correct average consensus value for every node in the network. For a network with loops, we convert the weighted average problem into an optimization problem with a relaxation factor whose solution approaches to the weighted average with appropriate relaxation factor. A modified algorithm is also proposed for loopy networks and consensus will be reached asymptotically with low computation complexity and fast convergence rate.