A Student's t filter for heavy tailed process and measurement noise

We consider the filtering problem in linear state space models with heavy tailed process and measurement noise. Our work is based on Student's t distribution, for which we give a number of useful results. The derived filtering algorithm is a generalization of the ubiquitous Kalman filter, and reduces to it as special case. Both Kalman filter and the new algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter.