Non-identity measurement models for orientation estimation based on directional statistics

We propose a novel measurement update procedure for orientation estimation algorithms that are based on directional statistics. This involves consideration of two scenarios, orientation estimation in the 2D plane and orientation estimation in three-dimensional space. We make use of the von Mises distribution and the Bingham distribution in these scenarios. In the derivation, we discuss directional counterparts to the extended Kalman filter and a statistical-linearization-based filter. The newly proposed algorithm makes use of deterministic sampling and can be thought of as a directional variant of the measurement update that is used in well-known sample-based algorithms such as the unscented Kalman filter.