Linear Optimal Estimators for Systems With Multiplicative Noises and Time-Correlated Additive Noise

This paper is concerned with the state estimation problem for systems with state multiplicative noise, measurement multiplicative noise and time-correlated additive measurement noise. The multiplicative noises are uncorrelated white noises with zero means. Time-correlated measurement noise is described by a linear model with Gauss white noise. Based on a measurement difference method, the linear optimal estimators including filter, multi-step predictor and multistep smoother are derived in the linear minimum variance (LMV) sense. The proposed estimators are recursive. They do not require the inverse of the state transition matrix. The simulation research verifies the effectiveness of the proposed algorithms.