On averaging rotations
On averaging rotations
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DOI：
10.1023/a:1011217513455
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发表时间：
2001-01-01
影响因子：
2
通讯作者：
Gramkow, C
中科院分区：
文献类型：
--
作者：
Gramkow, C
在本文中，将两种常见的平均旋转方法与基于黎曼度量的更先进的方法进行了比较。通常，表示旋转的四元数或矩阵的重心被用作平均值的估计。这些方法忽略了旋转属于非线性流形，必须应用重新归一化或正交化才能获得正确的旋转。后面的这些步骤被视为对假设向量空间引入的错误的临时校正。文章表明，这两种近似方法可以从黎曼度量的自然近似中推导出来，并且后续的修正是最小二乘估计所固有的。
In this paper two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very often the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong to a non-linear manifold and re-normalization or orthogonalization must be applied to obtain proper rotations. These latter steps have been viewed as ad hoc corrections for the errors introduced by assuming a vector space. The article shows that the two approximative methods can be derived from natural approximations to the Riemannian metric, and that the subsequent corrections are inherent in the least squares estimation.