Centralized and Distributed Variational Bayesian Robust Kalman Filter Under Elliptical Distribution With Inaccurate Noise Covariance Matrices

This paper focuses on centralized and distributed state estimations with measurement outliers and inaccurate noise covariance matrices. To capture the heavy-tailed nature introduced by measurement outliers, the measurement noise is modeled using an elliptical distribution (ED). To guarantee the conjugate, the inaccurate scale matrix of ED and the covariance matrix of the Gaussian process noise are modeled as inverse Wishart distributions, respectively. In the centralized filtering algorithm, enabling robust multi-sensor fusion at a central node, the state and parameters are jointly estimated based on the variational Bayesian (VB) approach. In the distributed case, a distributed VB (DVB) algorithm is proposed in a fully distributed way, which includes the natural gradient ascent, consensus averaging, and VB updates. Simulation results demonstrate that the proposed algorithms substantially outperform existing state-of-the-art filters in terms of robustness and estimation accuracy.