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.
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