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Unscented Orientation Estimation Based on the Bingham Distribution

机译：基于Bingham分布的无味方向估计

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In this work, we develop a recursive filter to estimate orientation in 3D, represented by quaternions, using directional distributions. Many closed-form orientation estimation algorithms are based on traditional nonlinear filtering techniques, such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). These approaches assume the uncertainties in the system state and measurements to be Gaussian-distributed. However, Gaussians cannot account for the periodic nature of the manifold of orientations and thus small angular errors have to be assumed and ad hoc fixes must be used. In this work, we develop computationally efficient recursive estimators that use the Bingham distribution. This distribution is defined on the hypersphere and is inherently more suitable for periodic problems. As a result, these algorithms are able to consistently estimate orientation even in the presence of large angular errors. Furthermore, handling of nontrivial system functions is performed using an entirely deterministic method which avoids any random sampling. A 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 orientations.
机译：在这项工作中，我们开发了一种递归滤波器，以使用方向分布来估计由四元数表示的3D方向。许多闭合形式的方向估计算法都基于传统的非线性滤波技术，例如扩展卡尔曼滤波器（EKF）或无味卡尔曼滤波器（UKF）。这些方法假定系统状态和测量值的不确定性为高斯分布。但是，高斯人无法解释取向流形的周期性，因此必须假定较小的角度误差，并且必须使用临时固定。在这项工作中，我们开发使用Bingham分布的高效计算递归估计器。这种分布在超球面上定义，并且固有地更适合于周期性问题。结果，即使在存在大角度误差的情况下，这些算法也能够一致地估计取向。此外，使用可避免任何随机采样的完全确定性的方法来执行非平凡的系统功能。提出了一种类似于UKF的方案，用于定向的非线性流形。这是第一个确定性采样方案，可以真正反映方向的非线性流形。

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