State estimators for systems with random parameter matrices, stochastic nonlinearities, fading measurements and correlated noises

Using the innovation analysis approach, the optimal linear state estimators, including the filter, predictor and smoother, in the linear minimum variance (LMV) sense are presented for a class of nonlinear discrete-time stochastic uncertain systems with fading measurements and correlated noises. Stochastic uncertainties of parameter matrices are depicted by correlated multiplicative noises. Stochastic nonlinearities are characterized by a known conditional mean and covariance. Different sensor channels have different fading measurement rates. The process and measurement noises are finite-step auto- and/or cross-correlated with each other. Two simulation examples verify the effectiveness of the proposed algorithms.