Solution of Nine-Parameter Affine Transformation Based on Quaternions
Publication: Journal of Surveying Engineering
Volume 147, Issue 3
Abstract
A least-squares solution for (a)symmetric nine-parameter three-dimensional affine coordinate transformation based on quaternions is presented. Retrieval of the nine transformation parameters (three translations, three scale factors, and three Euler rotation angles) and their covariance matrix from the quaternion-based estimates is given in detail. The proposed method can successfully handle all the cases regardless of the magnitude of the parameters and full covariance matrices of the control points. Efficiency and consistency of the solution are discussed within five different case studies consisting of many numerical examples.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The third author thanks the YTU Rectorate for supplying academic license for MATLAB 2017a.
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Published In
Journal of Surveying Engineering
Volume 147 • Issue 3 • August 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Sep 18, 2020
Accepted: Apr 5, 2021
Published online: Jun 1, 2021
Published in print: Aug 1, 2021
Discussion open until: Nov 1, 2021
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