Total Least-Squares Estimation for 2D Affine Coordinate Transformation with Constraints on Physical Parameters
Publication: Journal of Surveying Engineering
Volume 142, Issue 3
Abstract
The error-in-variable (EIV) model takes the error of all variables into account and has been widely applied to many practical problems arising in environmental study, geology, geographic information science (GIS), and geodesy. Coordinate transformations are among the most frequently encountered problems in spatial data processing, and the EIV model can be built based on two sets of coordinates. In some applications, physical parameters—such as the shift, rotation angle, and scale factor—have constraints. Current implementations of the constrained EIV (CEIV) model do not consider physical constraints explicitly. The purpose of this paper is to convert physical constraints into mathematical forms and to use constrained total least squares (CTLS) to solve the CEIV problem of two-dimensional (2D) affine transformation. The effectiveness of this method is illustrated through a numerical example.
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Acknowledgments
The authors appreciate the anonymous reviewer’s valuable comments and clarification of this manuscript. The work described in this paper was supported by the National Natural Science Foundation of China (Project 41174003).
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Published In
Journal of Surveying Engineering
Volume 142 • Issue 3 • August 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Feb 4, 2015
Accepted: Dec 22, 2015
Published online: Feb 8, 2016
Discussion open until: Jul 8, 2016
Published in print: Aug 1, 2016
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