Partial Total-Least-Squares Adjustment of Condition Equations with Application to a Rectangular Building Adjustment in a GIS
Publication: Journal of Surveying Engineering
Volume 144, Issue 1
Abstract
This paper presents a partial total-least-squares adjustment method for condition equations (PTLSC) in which the observation vector and coefficient matrix contain linearly correlated errors. In the proposed method, the functionally independent variables in the observation vector and the coefficient matrix of the condition equations are abstracted to form a collected observation vector. The PTLSC method is formulated by minimizing the sum of the weighted squared errors of the collected observation vector by the use of a Lagrangian multiplier algorithm. The estimation of the covariance matrix based on linear approximation for the collected observation vector is also derived. The proposed PTLSC method was tested in an example of rectangular building adjustment in a geographical information system (GIS). The results indicate that the proposed PTLSC method can adjust the interior angles of the digitized buildings so they are right angles, and it can be used to maintain the correlations among the elements in the observation vector and the coefficient matrix.
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Acknowledgments
The authors thank the editor and the anonymous reviewers for their valuable comments for the improvement of the paper. The work described in this paper was substantially supported by the National Natural Science Foundation of China (Projects Nos. 41601414, 41325005, and 41631178), Shanghai Sailing Program (Project No. 16YF1412200), National Key Research and Development Program of China (Projects Nos. 2017YFB0502903, 2016YFC0803107-02), and Fundamental Research Funds for the Central Universities.
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Published In
Journal of Surveying Engineering
Volume 144 • Issue 1 • February 2018
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Apr 2, 2014
Accepted: Sep 13, 2017
Published online: Nov 17, 2017
Published in print: Feb 1, 2018
Discussion open until: Apr 17, 2018
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