Optimal Kalman-like filter for a class of nonlinear stochastic systems

This paper deals with an optimal Kalman-like filter for nonlinear discrete-time systems aided with auto and cross-correlated noises and stochastic parameter matrices involved in state and measurement equations, and random nonlinearity. The random variables are proposed by their statistical characteristics while the inquiry is focused on stochastic multivariate analysis and calculation. For the nonlinear system with the auto and cross-correlated noises and stochastic parameter matrices, an equivalent system is first reconstructed by decomposing stochastic parameter matrices and introducing uncorrelated pseudo-noises. Then a recursive filter that ensures unbiasedness and minimizes the error variance is designed for the newly transformed equivalent system. Finally, the filter is verified by applying it to some numerical simulations.