A Novel Robust Kalman Filter Based on Switching Gaussian-Heavy-Tailed Distribution

In this brief, the state estimation problems of systems with unknown non-stationary heavy-tailed noises are investigated. First, we present a new switching Gaussian-heavy-tailed (SGHT) distribution, which can model the noises by adaptive learning of the switching probability between the Gaussian distribution and the newly designed heavy-tailed distribution. Then, the SGHT distribution is expressed as a hierarchical Gaussian presentation by utilizing two auxiliary variables satisfying the categorical distribution and the Bernoulli distribution respectively. After-wards, a new SGHT distribution based robust Kalman filter (SGHT-RKF) is derived by applying the variational Bayesian (VB) inference. Finally, the simulations are performed to illustrate the superior performance of the developed filter as compared with existing filters.