A Robust Kalman Filter via Gamma Student’s t-Mixture Distribution Under Heavy-Tailed Measurement Noise

In order to increase the accuracy of the state estimation with nonstationary heavy-tailed measurement noises by correcting the mean vector and covariance matrix of Student’s t distribution, the gamma Student’s t (GaST) distribution is proposed. In the proposed GaST, a shape parameter modeled as Gaussian distribution and an auxiliary variable modeled as gamma distribution are introduced into the Student’s t distribution, and the mean vector and covariance matrix of Student’s t distribution can be estimated by learning the shape parameter and the auxiliary variable. Based on the GaST distribution, which can be written as a hierarchical Gaussian structure and the variational Bayesian approach, a GaST distribution-based Kalman filter (KF) is proposed. The simulation results show that the proposed KF possesses better accuracy compared to the existing best KFs for a state-space model with nonstationary heavy-tailed measurement noise. The effectiveness of the proposed KF is also demonstrated in the field experiments for mobile robot localization.