A novel IMM Kalman filter with colored multi-outlier non-stationary heavy-tailed measurement noise and uncertain state model

Abstract

A novel interactive multi-model (IMM) Kalman filter is proposed in this paper for the dynamic estimation with colored multi-outlier non-stationary heavy-tailed measurement noise (MNHMN) and uncertain state model. Firstly, the filtering problem with colored MNHMN is converted to the filtering problem with white MNHMN using the measurement difference method and the state expansion approach. To fully fit the multi-outlier non-stationary heavy-tailed property of the white MNHMN, a generalized Gaussian–Student's t mixture (GSTM) distribution is proposed, through which each dimension of the noise is independently modeled as a GSTM distribution. Meanwhile, a multivariate Bernoulli variable is introduced to construct a hierarchical Gaussian model, while the variational Bayesian (VB) technique is used to estimate the system state and the distribution parameters of noise collectively. The IMM method is adopted to deal with state model uncertainty, and a new model conditional likelihood function based on the proposed measurement noise model is derived through the variational lower bound theory. Thus, the lack of an analytical likelihood in the proposed generalized GSTM distribution is effectively resolved. Simulation results demonstrate the effectiveness of the proposed method.