Networked State Estimation for Two-Dimensional Systems with Multiplicative Noises and Observation Delays: An Iterative Coupled Estimator Design

Abstract

This article addresses the state estimation problem for a class of networked 2-D systems subject to autocorrelated multiplicative noises and multistep observation delays. The autocorrelated multiplicative noises are characterized as a linear system corrupted by additive white noises, and the multistep observation delays are described by the instantaneous and delayed output equations. The globally coupled correlation terms are first introduced to deal with the autocorrelated multiplicative noises, and then, a novel observation reconstruction approach is proposed to tackle the difficulty induced by multistep observation delays. By utilizing the space equivalence verification, it is shown that the reconstructed delay-free observation sequence retains the same information as the original delayed observation sequence. The purpose of this article is to design an iterative coupled estimator based on the globally coupled correlation terms and the reconstructed observation sequence. By means of the mathematical induction technique, it is demonstrated that the proposed estimator preserves the property of unbiasedness. Moreover, the estimator gains are obtained by minimizing the estimation error covariance, and some sufficient conditions are derived to guarantee the existence of an upper bound for the estimation error covariance in the mean square sense. Finally, a numerical example is provided to verify the effectiveness of the proposed estimation scheme.