Gaussian filter for nonlinear stochastic uncertain systems with correlated noises

In this paper, a nonlinear Gaussian filter is designed for nonlinear stochastic uncertain system with correlated noises. Because the networked systems with random delays and packet losses can be transformed into those with correlated multiplicative noises in the state and measurement matrices, we consider the stochastic uncertain system with synchronously correlated multiplicative noises. The process and observation additive noises are one-step autocorrelated, respectively. Process and observation noises are two-step forward cross-correlated. Based on the abovementioned conditions, we proposed a nonlinear Gaussian recursive filter by using an alternative formulation and a new cubature Kalman filter is given on the basis of the third-degree spherical-radial rule. In order to compare with the algorithm proposed in this paper, a new version based on the extended Kalman filter is developed in Appendix B. In the simulation part, we give two simulation examples to show the effectiveness of the proposed algorithm.