Distributed recursive filtering for multi-sensor networked systems with multi-step sensor delays, missing measurements and correlated noise

Abstract

This paper is concerned with the distributed recursive filtering for the discrete-time nonlinear multi-sensor networked system with multi-step sensor delays, missing measurements and correlated noise. Based on the innovation statistical distance, an adaptive time delay estimation method, which belongs to the online methods, is derived to determine whether the measurement is acquired or not along with the time delay step. Then, a nonlinear system model is founded based on a set of selected Bernoulli distributed random variables to describe the multi-step sensor delays, missing measurements and correlated noise. The obtained time delay step can be used to update parameters of the proposed measurement model. Next, a distributed recursive filtering is designed based on linear fitting (LF) and weighted average consensus (WAC) to solve the nonlinear state estimation in the multi-sensor networked system. Meanwhile, a selection strategy is designed based on the innovation statistical distance for the weighted factors to improve the distributed fusion accuracy. Further, filtering errors of the distributed recursive filtering are proved to be exponentially bounded in mean square. Numerical simulations are conducted to evaluate the performance of the proposed algorithm.