Tracking 3-D Rotations with the Quaternion Bingham Filter

Abstract

A deterministic method for sequential estimation of 3-D rotations is presented. The Bingham distribution is used to represent uncertainty directly on the unit quaternion hypersphere. Quaternions avoid the degeneracies of other 3-D orientation representations, while the Bingham distribution allows tracking of large-error (high-entropy) rotational distributions. Experimental comparison to a leading EKF-based filtering approach on both synthetic signals and a ball-tracking dataset shows that the Quaternion Bingham Filter (QBF) has lower tracking error than the EKF, particularly when the state is highly dynamic. We present two versions of the QBF, suitable for tracking the state of first- and second-order rotating dynamical systems.