Outlier-Robust Centralized and Distributed Variational Bayesian Moving Horizon Estimation

This paper addresses robust adaptive state estimation for a linear dynamical system subject to measurement outliers and Gaussian noises with unknown time-varying covariances. The proposed method relies on a Bernoulli-Gaussian (BG) model of measurement noise as well as on a variational Bayesian-moving horizon estimation (VB-MHE) approach that allows to jointly estimate the state trajectory on a moving window of fixed size along with the noise parameters (outlier probability, process noise and measurement noise covariances). A centralized robust adaptive filter is first derived and then extended to the distributed multi-sensor case by exploiting a distributed variational Bayesian (DVB) approach. It is shown, via simulation experiments, how the performance of both proposed, centralized and distributed, robust adaptive filters is very close to the ideal one achievable by a Kalman filter with perfect outlier detection and full knowledge of noise covariances.