An Outlier-Robust Kalman Filter

We introduce a novel approach for processing sequential data in the presence of outliers. The outlier-robust Kalman filter we propose is a discrete-time model for sequential data corrupted with non-Gaussian and heavy-tailed noise. We present efficient filtering and smoothing algorithms which are straightforward modifications of the standard Kalman filter Rauch-Tung-Striebel recursions and yet are much more robust to outliers and anomalous observations. Additionally, we present an algorithm for learning all of the parameters of our outlier-robust Kalman filter in a completely unsupervised manner. The potential of our approach is borne out in experiments with synthetic and real data.