Recursive Estimation of Orientation Based on the Bingham Distribution

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

Unscented Orientation Estimation Based on the Bingham Distribution

Orientation estimation for 3D objects is a common problem that is usually tackled with traditional nonlinear filtering techniques such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). Most of these techniques assume Gaussian distributions to account for system noise and uncertain measurements. This distributional assumption does not consider the periodic nature of pose and orientation uncertainty. We propose a filter that considers the periodicity of the orientation estimation problem in its distributional assumption. This is achieved by making use of the Bingham distribution, which is defined on the hypersphere and thus inherently more suitable to periodic problems. Furthermore, handling of non-trivial system functions is done using deterministic sampling in an efficient way. A deterministic sampling scheme reminiscent of the UKF is proposed for the nonlinear manifold of orientations. It is the first deterministic sampling scheme that truly reflects the nonlinear manifold of the orientation

Directional statistics and filtering using libDirectional

In this paper, we present libDirectional, a MATLAB library for directional statistics and directional estimation. It supports a variety of commonly used distributions on the unit circle, such as the von Mises, wrapped normal, and wrapped Cauchy distributions. Furthermore, various distributions on higher-dimensional manifolds such as the unit hypersphere and the hypertorus are available. Based on these distributions, several recursive filtering algorithms in libDirectional allow estimation on these manifolds. The functionality is implemented in a clear, well-documented, and object-oriented structure that is both easy to use and easy to extend