A Novel Robust Kalman Filter With Non-stationary Heavy-tailed Measurement Noise

A novel robust Kalman filter based on Gaussian-Student's t mixture (GSTM) distribution is proposed to address the filtering problem of a linear system with non-stationary heavy-tailed measurement noise. The mixing probability is recursively estimated by using its previous estimates as prior information, and the state vector, the auxiliary parameter, the Bernoulli random variable and the mixing probability are jointly estimated utilizing the variational Bayesian method. The excellent performance of the proposed robust Kalman filter, compared with the existing state-of-the-art filters, is illustrated by a target tracking simulation results under the case of non-stationary heavy-tailed measurement noise.