Improved Cubature Kalman Filter for High-Dimensional Systems with Multiplicative Noises

Abstract

It is a challenging mission to estimate accurately the state of a non-cooperative spacecraft with multiplicative noises. In this paper, an improved cubature Kalman filter for nonlinear systems with multiplicative noises (ICKF_M) is proposed. First, based on the assumption that multiplicative noise satisfies the Gaussian distribution, the conditional mean variance of multiplicative noise is considered in the prediction and updating process. According to the Bayesian estimation theory, the conditional probability density distribution of multiplicative noise is added to the prediction and update functions to adapt the multiplicative noise. Then, to solve the defect of cubature Kalman filter (CKF), a new method for generating sigma points is designed instead of the classical methods, which has transformed the posterior sigma-points error matrix from prediction phase to the posterior domain of update. Finally, a binocular visual method is used to measure the state of the spacecraft. Compared with the previous methods, the simulation results indicate that the average norm of estimation error has nearly decreased by 20% in comparison with the similar filters in the reference. Moreover, the convergence rate of the proposed algorithm is obviously faster than that of the previous algorithm.