Recursive Estimation of Orientation Based on the Bingham Distribution

TL;DR

This paper introduces a recursive filtering method based on the Bingham distribution for directional data, effectively handling 2D and 3D orientation estimation problems with symmetry considerations and real-time applicability.

Contribution

It presents a novel recursive filter for directional data using the Bingham distribution, extendable to 3D orientations with quaternion support.

Findings

Outperforms traditional Kalman filter in directional estimation scenarios

Handles 180-degree symmetry in circular filtering problems

Suitable for real-time orientation tracking applications

Abstract

Directional estimation is a common problem in many tracking applications. Traditional filters such as the Kalman filter perform poorly because they fail to take the periodic nature of the problem into account. We present a recursive filter for directional data based on the Bingham distribution in two dimensions. The proposed filter can be applied to circular filtering problems with 180 degree symmetry, i.e., rotations by 180 degrees cannot be distinguished. It is easily implemented using standard numerical techniques and suitable for real-time applications. The presented approach is extensible to quaternions, which allow tracking arbitrary three-dimensional orientations. We evaluate our filter in a challenging scenario and compare it to a traditional Kalman filtering approach.