An improved Gaussian filter with randomly delayed measurements and synchronously correlated noises

The classical Gaussian filters are based on the assumption that measurements are acquired in time and noises of process and measurement are independent of each other. However, this assumption is sometimes hard to satisfy in practical applications. In this paper, an optimal estimation algorithm in the form of Gaussian filter framework is designed to solve the problem of states estimation of a Gaussian system with randomly delayed measurements and synchronously correlated noises, and the rule of third-degree spherical-radial cubature is employed to deduced the suboptimal estimation implementation of the proposed algorithms which is named cubature Kalman filter with randomly delayed measurements and synchronously correlated noises (CKF-RDSCN). It takes random sequence of Bernoulli to describe the possible situation with respect to random delay in observation measurement and the property of Gaussian conditional distribution is utilized to solve the problem of noises correlation. Simulation results demonstrate that CKF-RDSCN is more accurate and stability than the extended Kalman filter (EKF), unscented Kalman filter (UKF) and CKF in the states estimation problem involved with randomly delayed measurements and synchronously correlated noises.