Alternative framework of the Gaussian filter for non-linear systems with randomly delayed measurements and correlated noises

Compared with the normal Gaussian filter that measurements are acquired in real-time and process and measurement noises are independent, the authors study a class of non-linear state estimation problems with one-step randomly delayed measurements and correlated noises. Using a novel alternative framework, where the process and measurement noises are as the augment of the state vector, the author can deduce the related formula and get a novel filtering algorithm. In order to explain the feasibility of the proposed algorithm, this study demonstrates that the relevant recursive formula satisfies the Gaussian distribution. In order to explain the rationality of the proposed algorithm, the relevant union estimation form is given in Section 1. For the sake of facilitating computer simulation, the sub-optimal realisation of the proposed algorithm on the basis of the spherical-radial rule is given, which is alternative framework Gaussian filter with the correlated noise and delayed measurements. The superiority of the algorithm presented, compared with the other algorithm, is shown in the end of this study.