Robust Kalman Filter for Systems With Colored Heavy-Tailed Process and Measurement Noises

In this brief, we consider the robust state estimation for a linear system with colored heavy-tailed process and measurement noises. We employ the state augmentation and measurement differencing methods to whiten the colored noise and use the Student’s t distribution to model the heavy-tailed property, which makes a new state space model with the augmented state vector. The posterior estimation of the system state, inaccurate scale matrices, and auxiliary parameters are jointly inferred with the variational Bayes method by constructing the hierarchical Gaussian forms of the prediction and likelihood probability density functions and selecting the proper prior distributions of the scale matrices and auxiliary parameters. A typical target tracking simulation is given to confirm the performance of the proposed robust Kalman filter.