An improved Gaussian filter with Asynchronously correlated noises

In order to increase the accuracy of state estimation for a nonlinear discrete-time system with asynchronously correlated noises, an improved Gaussian filter(GF) is proposed. Different from the traditional methods for this issue, which reconstruct process equation to make process noises and measurement noises uncorrelated, the novel algorithm of GF directly utilizes the correlation information to obtain more accurate estimation. And the computation of integrals with random variables, which is the core problem involved in the case of asynchronously correlated noises, it employs Stirling´s interpolation to solve it. Furthermore, based on the novel GF framework, a new cubature Kalman filter with asynchronously correlated noises(CKF-ACN) is developed by the rule of spherical-radial cubature. Simulation results demonstrate the superior performance of the proposed CKF-ACN in contrast to the extended Kalman filter with asynchronously correlated noises and the CKF.