Recursive state estimation for linear systems with lossy measurements under time-correlated multiplicative noises

Abstract

This paper is concerned with the recursive state estimation problem for a class of linear discrete-time systems with lossy measurements and time-correlated multiplicative noises (TCMNs). The lossy measurements result from one-step transmission delays and packet dropouts. Different from the traditional white multiplicative noises, TCMNs are included in the measurement model in order to reflect engineering practice. Utilizing the state augmentation approach, the system under investigation is first converted into a stochastic parameter system, and some new recursive terms (including the estimation for the product of state and multiplicative noises) are introduced to handle the difficulties caused by the TCMNs. Then, by the well-known projection theorem, recursive state estimation algorithms are developed in the sense of minimum mean-square error, which facilitate the design of the filter, the multi-step predictor and the smoothers. The proposed algorithms are explicitly dependant on the key system parameters including the covariances of the TCMNs, the occurrence probabilities of the transmission delays and the packet losses. Finally, simulation results illustrate the effectiveness of the presented estimation algorithms.