Publication
On Cayley's factorization with an application to the orthonormalization of noisy rotation matrices
Journal Article (2019)
Journal
Advances in Applied Clifford Algebras
Pages
49
Volume
29
Doc link
https://doi.org/10.1007/s00006-019-0965-0
File
Abstract
A real orthogonal matrix representing a rotation in four dimensions can be decomposed into the commutative product of a left- and a right-isoclinic rotation matrix. This operation, known as Cayley's factorization, directly provides the double quaternion representation of rotations in four dimensions. This factorization can be performed without divisions, thus avoiding the common numerical issues attributed to the computation of quaternions from rotation matrices. In this paper, it is shown how this result is particularly useful, when particularized to three dimensions, to re-orthonormalize a noisy rotation matrix by converting it to quaternion form and then obtaining back the corresponding proper rotation matrix. This re-orthonormalization method is commonly implemented using the Shepperd-Markley method, but the method derived here is shown to outperform it by returning results closer to those obtained using the Singular Value Decomposition which are known to be optimal in terms of the Frobenius norm.
Categories
robots.
Author keywords
Rotation matrices, quaternions, double quaternions, Cayley's factorization, Shepperd-Markley method
Scientific reference
S. Sarabandi, A. Perez and F. Thomas. On Cayley's factorization with an application to the orthonormalization of noisy rotation matrices. Advances in Applied Clifford Algebras, 29: 49, 2019.
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