Robust Gaussian Kalman Filter With Outlier Detection

We consider the nonlinear robust filtering problem where the measurements are partially disturbed by outliers. A new robust Kalman filter based on a detect-and-reject idea is developed. To identify and exclude outliers automatically, each measurement is assigned an indicator variable, which is modeled by a beta-Bernoulli prior. The mean-field variational Bayesian method is then utilized to estimate the state of interest as well as the indicator in an iterative manner at each time instant. Simulation results reveal that the proposed algorithm outperforms several recent robust solutions with higher computational efficiency and better accuracy.