Optimal recursive estimation for networked stochastic uncertain systems with fading measurements and time-correlated channel noises

This paper is concerned with the optimal linear estimation problem for discrete-time stochastic system with time-correlated channel noises, correlated multiplicative noises and fading measurements. The time-correlated channel noises are described by a seemingly ARMA (autoregressive moving average) model. By an equivalent transformation, the original system is transformed into the same-dimension system with finite-step correlated virtual noises and multiple measurement delays. The statistical properties of correlation functions among noise, state and measurement are analyzed. Further, the optimal linear state estimators including filter, predictor and smoother are derived by using an innovation analysis approach. A simulation example shows the effectiveness of the proposed algorithms.