A robust and efficient cubature Kalman filter based on the variational Bayesian method and its application in target tracking

In this paper, we propose a robust cubature Kalman filter (CKF) for nonlinear state-space models with unknown state and measurement noise covariance matrix. We study situations in which sensors are independent of each other. Therefore, the unknown measurement noise variance is modeled as an unknown inverse gamma (IG) distribution. The Gaussian-Student-t-inverse-Wishart (GSTIW) mixture distribution is used to model the one-step prediction distribution. Modeling generates numerous unknown parameters. Therefore, we adopt the statistical linearization method to linearize the observation function and then estimate the state and parameters separately to reduce the computational burden of estimating unknown parameters, significantly improving the algorithm's efficiency. Finally, using the variational Bayesian method, a novel and efficient robust CKF based on the IG distribution and GSTIW mixture distributions (IG-GSTIW-CKF) is obtained. Simulation and experimental results show that the proposed method has better estimation accuracy than several advanced algorithms when sensors are independent. In addition, the efficiency of the proposed algorithm is significantly higher than that of other CKF-based methods.