Variational Bayesian Kalman Filter Based on MPR Parameterization and Mode Switching Criteria

In this article, a variational Bayesian (VB) adaptive Kalman filter (KF) based on the model parameter ratio (MPR) and mode switching criteria is proposed for estimating unknown and time-varying noise covariance matrices (NCMs). Different from existing methods, the adaptive KF proposed in this article can achieve parameterized processing and dimensionality reduction estimation of NCMs. First, the estimation of the NCMs is reduced to a 1-D estimation of the ratio coefficient based on MPR to enhance stability and accuracy. Second, the parameterized configuration can be learned during VB inference without relying on external algorithms. The convergence of the ratio coefficients and parameterized configurations is analyzed within a VB framework using coordinate-ascent variational inference (CAVI). Third, a mode switching mechanism based on innovation-consistency convergence is designed to cope with initial uncertainty and numerical instability during the filtering process. Finally, the proposed algorithm is verified by numerical simulation and physical experiments to demonstrate its feasibility and effectiveness.