A Robust Kalman Filter with Bias Estimation Based on Variational Bayesian Inference and Chi-Square Test

This article proposes a robust Kalman filter for a linear state-space model (SSM) in the present of heavy-tailed non-Gaussian measurement noise with time-varying bias. The filter primarily consists of a main estimator, a reference estimator and a method for fusing them. The measurement noise distribution is modeled as a new Student’s t-Normal-Wishart distribution, and then the hierarchical Gaussian SSM is established. The main estimator is derived by variational Bayesian inference, in which the state and bias variables are estimated simultaneously. The reference estimator is introduced to further improve the state estimation accuracy of the main estimator using chi-square test. Simulation results demonstrate the effectiveness and superiority of the proposed method.