Finite‐horizon estimation for 2‐D systems with time‐correlated multiplicative noises: A recursive iterative coupled estimator design

Abstract This paper addresses the state estimation problem for a class of two‐dimensional shift‐varying systems with time‐correlated multiplicative measurement noises and additive noises. The time‐correlated multiplicative noises can be described as a linear system model corrupted by white noise. The main objective of this paper is to propose a recursive iterative coupled new‐type estimators and design the estimated gain reasonably to guarantee the minimum error covariance at each step. First, two new‐type coupling estimators are designed by introducing a new term. The unbiasedness of the two estimators are guaranteed by resorting to the mathematical inductive approach. Subsequently, an effective estimation is proposed given initial conditions. Moreover, the boundedness performance is investigated of the error covariance, and an upper bound is given based on the spectral norm. Finally, two numerical example are presented as an example to show the effectiveness of the estimation algorithm.