Variational Bayesian and generalized maximum-likelihood based adaptive robust nonlinear filtering framework - Yang, Baojian; Wang, Huaiguang; Shi, Zhiyong (Signal processing, 2024)
•A variational Bayesian based cubature Kalman filter (VBCKF-R) is derived.•An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation).•The VBCEECKF algorithm is developed by applying the CEE criteria to the proposed adaptive robust nonlinear filtering framework.•The proposed VBCEECKF algorithm has high precision in target tracking under non-ideal measurement situations. An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation) to simultaneously handle the outliers and uncertain measurement noise covariance matrix (MNCM) for state estimation. This framework utilizes the cubature criterion to solve nonlinear integration problems. By embedding GM estimation in the VB method, the uncertain MNCM is modified while robust estimation is performed. The modified MNCM also provides more accurate model parameters for GM estimation, achieving the unity of adaptability and robustness. The VBCEECKF algorithm was obtained by applying the strong robust centered error entropy criterion to the adaptive robust nonlinear filtering framework. The simulation results of target tracking under different noise conditions verify the superiority of the adaptive robust filter compared to existing methods.