Design and implementation of Gaussian filter for nonlinear system with randomly delayed measurements and correlated noises

In this paper, we focus on the nonlinear state estimation problem with both one-step randomly delayed measurements and correlated noises. Firstly, a general framework of Gaussian filter is designed under Gaussian assumption on the conditional density. Furthermore, the implementation of Gaussian filter is transformed into the computation of the nonlinear numerical integrals in the proposed framework. Secondly, a new cubature Kalman filtering (CKF) algorithm is developed on the basis of the spherical-radial cubature rule for approximating such nonlinear integrals. Finally, the performance of the modified CKF is verified by a numerical simulation example.