Comparison of Structured and Weighted Total Least-Squares Adjustment Methods for Linearly Structured Errors-in-Variables Models
Publication: Journal of Surveying Engineering
Volume 143, Issue 1
Abstract
The paper focuses on a specific errors-in-variables (EIV) model named the linearly structured EIV (LSEIV) model in which all the random elements of design matrix are in a linear combination of an input vector with random errors. Two existing structured total least-squares (STLS) algorithms named constrained TLS (CTLS) and structured TLS normalization (STLN) are introduced to solve the LSEIV model by treating the input and output vectors as the noisy structure vectors. For comparison purposes, the weighted TLS (WTLS) method is also performed based on the partial EIV model. Approximated accuracy assessment methods are also presented. The plane fitting and Bursa transformation examples are illustrated to demonstrate the accuracy and computational efficiency performance of the proposed algorithms. It shows that the proposed STLS and WTLS algorithms can achieve the same accuracy if the dispersion matrix of the WTLS method is constructed based on the partial EIV model.
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Acknowledgments
The authors thank the anonymous reviewers for their valuable comments and constructive suggestions on this manuscript. The work was partially supported by the National Natural Science Foundation of China (41274012, 41404005, and 41474006).
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Journal of Surveying Engineering
Volume 143 • Issue 1 • February 2017
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© 2016 American Society of Civil Engineers.
History
Received: Mar 12, 2014
Accepted: Feb 18, 2016
Published online: May 9, 2016
Discussion open until: Oct 9, 2016
Published in print: Feb 1, 2017
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