A Gaussian multi-scale mixture model-based outlier-robust Kalman filter

In many practical applications, the unknown non-stationary heavy-tailed distributed process and measurement noises (HTPMNs) are prone to occur due to inaccurate noise prior and stochastic outliers. To achieve the state estimation under this situation, a new outlier-robust Kalman filter based on Gaussian multi-scale mixture model (GMSMM-ORKF) is proposed in this paper. First, a new GMSMM is designed to model the one-step prediction and measurement likelihood probability density functions. Then, the hierarchical prior presentation on the mixture probability vectors and scale parameters are built. Furthermore, employing the variational Bayesian (VB) inference, a GMSMM-ORKF is derived. Finally, a classical target tracking model and real navigation experiment are utilized to demonstrate the effectiveness of the proposed filter.