Recursive estimation for nonlinear stochastic systems with multi-step transmission delays, multiple packet dropouts and correlated noises

This paper is concerned with the recursive estimation problem for a class of discrete-time nonlinear stochastic systems with multi-step transmission delays, multiple packet dropouts and correlated noises. The stochastic nonlinearity is described by statistical means, and noises are assumed to be one-step autocorrelated and cross-correlated. To convert the original system into the nonlinear stochastic parameterized one, some new variables are firstly introduced. Then, by applying the innovation analysis approach, the optimal linear estimators including filter, multi-step predictor and smoother are presented. The proposed algorithms, which are dependent on the probabilities of delays and data losses, the matrices used to describe the stochastic nonlinearity as well as one-step correlation coefficient matrices, are expressed by the Riccati and Lyapunov equations. Furthermore, sufficient conditions are established to guarantee the convergence of the state covariance and the existence of the steady-state estimators for the time-invariant nonlinear systems. Finally, a simulation example is given to demonstrate the effectiveness of the proposed algorithms.