Gaussian/Gaussian‐mixture filters for non‐linear stochastic systems with delayed states
Xiaoxu Wang, Yan Liang, Quan Pan, He Huang · IET Control Theory and Applications · 2014
The Gaussian mixture approximation to the probability density function of the state is more appropriate than the single Gaussian approximation. A Gaussian mixture filter (GMF) is proposed for a class of non‐linear discrete‐time stochastic systems with the multi‐state delayed case. First, a novel non‐augmented filtering framework of the constituent Gaussian filter (GF) in GMF is derived, which recursively operates by analytical computation and non‐linear Gaussian integrals. The implementation of such GF is thus transformed to the computation of such non‐linear integrals in the proposed framework, which is solved by applying different numerical technologies for developing various variations of the non‐augmented GF, for example, GF‐cubature Kalman filter (CKF) based on the cubature rule. Secondly, a non‐augmented GMF is discussed by a weight sum of the above proposed GF, where each GF component is independent from the others and can be performed in a parallel manner, and its corresponding weigh is updated by using the measurements according to Bayesian formula. Naturally, a variation or implementation of such GMF based on the cubature rule is the GMF‐CKF. Finally, the performance of the new filters is demonstrated by a numerical example and a vehicle suspension estimation problem.