Robust Bayesian Filtering Using Bayesian Model Averaging and Restricted Variational Bayes

Bayesian filters can be made robust to outliers if the solutions are developed under the assumption of heavy-tailed distributed noise. However, in the absence of outliers, these robust solutions perform worse than the standard Gaussian assumption based filters. In this work, we develop a novel robust filter that adopts both Gaussian and multivariate t-distributions to model the outliers contaminated measurement noise. The effects of these distributions are combined within a Bayesian Model Averaging (BMA) framework. Moreover, to reduce the computational complexity of the proposed algorithm, a restricted variational Bayes (RVB) approach handles the multivariate t-distribution instead of its standard iterative VB (IVB) counterpart. The performance of the proposed filter is compared against a standard cubature Kalman filter (CKF) and a robust CKF (employing IVB method) in a representative simulation example concerning target tracking using range and bearing measurements. In the presence of outliers, the proposed algorithm shows a 38% improvement over CKF in terms of root-mean-square-error (RMSE) and is computationally 2.5 times more efficient than the robust CKF.