Estimating Variance–Covariance Matrix of the Parameters of a Fitted Triaxial Ellipsoid
Publication: Journal of Surveying Engineering
Volume 146, Issue 2
Abstract
Least-squares (LS) techniques have been a frequent choice advocated by a plethora of engineers for modeling problems requiring a unique solution based on sets of redundant observations perturbed by random noise. In this paper, several versions of LS procedures using the general quadric polynomial equation as the math model are reviewed and applied to a triaxial ellipsoid fitting exercise. The coefficients of this polynomial are then transformed into the nine parameters defining the spatial properties of the ellipsoid: semiaxes, coordinates of the origin, and rotation angles. Finally, a novel methodology requiring eigentheory is introduced to complete the determination of the variance–covariance matrices of these parameters.
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Data Availability Statement
The code (MATLAB scripts) used to process the results of this investigation can be found by interested readers in the Supplemental Data file that accompanies this article online or by writing directly to the corresponding author.
Acknowledgments
The authors thank the anonymous reviewers for their constructive comments, which significantly improved the quality of the original manuscript.
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Published In
Journal of Surveying Engineering
Volume 146 • Issue 2 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Nov 28, 2018
Accepted: Oct 2, 2019
Published online: Jan 29, 2020
Published in print: May 1, 2020
Discussion open until: Jun 29, 2020
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