Centralized and Distributed Robust State Estimation Over Sensor Networks Using Elliptical Distribution

Abstract

We consider the robust state estimation over sensor networks with non-Gaussian noise, which is often encountered in many applications. Motivated by the fact that the elliptical distribution is the natural extension of the Gaussian distribution and includes a variety of non-Gaussian distributions with heavy-tailed characteristics, we here adopt the elliptical distribution to model the heavy-tailed process and measurement noise. The general state evolution model is used to replace the process equation and the elliptical distribution is denoted as a Gaussian mixture form. Based on that, the posterior estimation of the system state together with the parameters of the process and measurement noises can be inferred by the variational Bayes method. Moreover, the corresponding distributed estimation algorithm is then provided, which enables distributed implementation. The target tracking over sensor networks is used to show the estimation accuracy of the proposed algorithms.