geometric_algebra
Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revisionNext revision | Previous revisionNext revisionBoth sides next revision | ||
geometric_algebra [2020/07/10 17:22] – [Articles] pbk | geometric_algebra [2020/07/19 17:12] – [Articles] pbk | ||
---|---|---|---|
Line 157: | Line 157: | ||
* [[https:// | * [[https:// | ||
* [[https:// | * [[https:// | ||
+ | * [[https:// | ||
* [[https:// | * [[https:// | ||
* [[https:// | * [[https:// | ||
Line 1300: | Line 1301: | ||
* [[https:// | * [[https:// | ||
Robust methods for finding the best rotation aligning two sets of corresponding vectors are formulated in the linear algebra framework, using tools like the SVD for polar decomposition or QR for finding eigenvectors. Those are well established numerical algorithms which on the other hand are iterative and computationally expensive. Recently, closed form solutions has been proposed in the quaternion’s framework, those methods are fast but they have singularities i.e., they completely fail on certain input data. In this paper we propose a robust attitude estimator based on a formulation of the problem in Geometric Algebra. We find the optimal eigen-quaternion in closed form with high accuracy and with competitive performance respect to the fastest methods reported in literature. | Robust methods for finding the best rotation aligning two sets of corresponding vectors are formulated in the linear algebra framework, using tools like the SVD for polar decomposition or QR for finding eigenvectors. Those are well established numerical algorithms which on the other hand are iterative and computationally expensive. Recently, closed form solutions has been proposed in the quaternion’s framework, those methods are fast but they have singularities i.e., they completely fail on certain input data. In this paper we propose a robust attitude estimator based on a formulation of the problem in Geometric Algebra. We find the optimal eigen-quaternion in closed form with high accuracy and with competitive performance respect to the fastest methods reported in literature. | ||
+ | |||
+ | * [[https:// | ||
+ | We develop a new framework for the study of generalized Killing spinors, where generalized Killing spinor equations, possibly with constraints, | ||
* [[https:// | * [[https:// |
geometric_algebra.txt · Last modified: 2024/06/03 18:10 by pbk