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

The article introduces a robust Kalman filter with bias estimation that leverages variational Bayesian inference and a chi-square test to enhance state estimation accuracy in systems with heavy-tailed non-Gaussian and nonzero-mean measurement noise. It presents a novel Student’s t-Normal-Wishart distribution to model heavy-tailed noise and a reference estimator to improve bias estimation during fast-changing bias tracking phases. The proposed filter demonstrates superior performance in simulations, showcasing better accuracy and robustness compared to existing methods. The integration of the reference estimator and the chi-square test for anomaly detection and bias compensation sets this work apart, offering a significant advancement in the field of robust state estimation.