Optimal Filtering for Two-Dimensional Nonlinear System with Stochastic Parameter Matrix in Measurement

This paper is concerned with the recursive minimum-variance filtering problem for a two-dimensional(2-D) system with known statistical characteristics of stochastic nonlinearity in state equation and stochastic parameter matrix in measurement equation. A two-step recursive filtering is proposed according to the innovation information. The obtained filtering is proved to be unbiased by applying mathematical induction and to minimize the error variance of state estimation at every step. The gain matrices of the optimal filter are designed by utilizing the complete-square method. Moreover, An algorithm for the optimal 2-D filtering is given to implement the computation.