Unscented Orientation Estimation Based on the Bingham Distribution

Abstract

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.

Bingham Distribution-Based Linear Filter for Online Pose Estimation

“…For example, Langevin distributions have been used for pose estimation [4,24]. Henebeck et al have recently developed a Bingham distribution-based recursive filtering approach for orientation estimation [9]. Glover et al [10] use Bingham distribution to describe the orientation features, while Hanebeck et al use this distribution for planar pose estimation [8].…”

“…The Bingham distribution is widely used to analyze paleomagnetic data [17], computer vision [12] and directional statistics [3] and recently in robotics [18,9,10,8].…”

“…where c ∈ R can be arbitrarily chosen as long as (Z + cI)) is negative definite [9]. Without loss of generality c = min(z i ) is chosen in this work.…”

“…If the pose was changing with time, then a suitable process model can be employed as shown in [9]. In this work, we focus on static pose estimation and hence do not need a process model to evolve the pose estimate over time.…”

“…The method uses a Bingham distribution-based filtering (BF) for orientation estimation and a Gaussian distribution for translation estimation. While there has been some recent work on using the BF for orientation estimation [18,9], there are some key differences compared to our approach. Firstly, prior work assumes that the state and measurements both are unit quaternions.…”