Design and Implementation of Gaussian Filter for Nonlinear System with Randomly Delayed Measurements and Correlated Noises

A new Gaussian approximate (GA) filter for nonlinear systems with one-step randomly delayed measurement and correlated noise is proposed in this paper. Firstly, a general framework of Gaussian filter is designed under Gaussian assumption on the conditional density. Then, the implementation of Gaussian filter is transformed into the approximation of the Gaussian weighted integral in the proposed frame. Secondly, a new cubature Kalman filtering(CKF)algorithm is developed on the basis of the spherical-radial cubature rule. The efficiency and superiority of the proposed method are illustrated in the numerical examples.