Accelerated corrective consensus: Converge to the exact average at a faster rate

Abstract-Averaging consensus algorithms provide an elegant, fully distributed, iterative way to compute the average of a set of measurements in a wireless sensor network. Unfortunately, they typically require a large number of iterations to reach convergence. Therefore, a great deal of effort has been devoted into accelerating consensus with improved accelerated consensus algorithms. Nevertheless, these techniques assume the communication graph is undirected with fixed or switching topologies, whereas actual low-power wireless networks present random and asymmetric packet losses. As a consequence, these methods might fail to converge to the correct average value when deployed in wireless sensor networks. In this paper we integrate accelerated consensus with corrective consensus, a technique that can compute the correct average of the measurements under random packet losses. Our simulation results show that the proposed accelerated corrective consensus converges to the correct average, presents a faster convergence rate than corrective consensus, and, for a similar number of iterations, it achieves convergence errors about 5,000 times smaller than accelerated consensus.