Simultaneous Perturbation Stochastic Approximation-based Consensus for Tracking under Unknown-but-Bounded Disturbances

Abstract

We consider a setup where a distributed set of sensors working cooperatively can estimate an unknown signal of interest, whereas any individual sensor cannot fulfil the task due to lack of necessary information diversity. This paper deals with these kinds of estimation and tracking problems and focuses on a class of simultaneous perturbation stochastic approximation (SPSA)-based consensus algorithms for the cases when the corrupted observations of sensors are transmitted between sensors with communication noise and the communication protocol has to satisfy a prespecified cost constraints on the network topology. Sufficient conditions are introduced to guarantee the stability of estimates obtained in this way, without resorting to commonly used but stringent conventional statistical assumptions about the observation noise such as randomness, independence, and zero mean. We derive an upper bound of the mean square error of the estimates in the problem of unknown time-varying parameters tracking under unknown but bounded observation errors and noisy communication channels. The result is illustrated by a practical application to the multi-sensor multi-target tracking problem.