Recursive nonlinear filtering for angular data based on circular distributions

Estimation of circular quantities is a widespread problem that occurs in many tracking and control applications. Commonly used approaches such as the Kalman filter, the extended Kalman filter (EKF), and the unscented Kalman filter (UKF) do not take periodicity explicitly into account, which can result in low estimation accuracy. We present a filtering algorithm for angular quantities in nonlinear systems that is based on circular statistics. The new filter switches between three different representations of probability distributions on the circle, the wrapped normal, the von Mises, and a Dirac mixture density. It can be seen as a systematic generalization of the UKF to circular statistics. We evaluate the proposed filter in simulations and show its superiority to conventional approaches.