Bias-Corrected Weighted Total Least-Squares Adjustment of Condition Equations
Publication: Journal of Surveying Engineering
Volume 141, Issue 2
Abstract
The total least-squares (TLS) method and its variations have recently received increasing research attention. However, little attention has been given to the weighted TLS adjustment method with condition equations. In this paper, a weighted TLS method designed for condition equations (WTLSC) is presented with the assumption that both the observation vector and design matrix contain errors. The covariance matrices are estimated for both the observation vector and design matrix after the adjustment, and the biases are corrected for the adjusted observation vector, design matrix, and corresponding covariance matrices in the WTLSC method. The proposed approach was used in an adjustment problem of an object point photographed by three terrestrial cameras. The results show that the proposed method resolves the condition equations with errors in the design matrix without linearization in the case study. The proposed WTLSC method generates stable error vector and matrix for the observation vector and design matrix, which satisfy the condition equation in the repeated simulation experiments. The results also show that there are biases in the adjusted observation vector, design matrix, and corresponding covariance matrices, although the biases are small in the case study.
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Acknowledgments
The authors thank the editors and anonymous reviewers for the constructive advice on the improvement of the paper. The work described in this paper was substantially supported by the National Natural Science Foundation of China (Project Nos. 41325005, 41171352, and 41174003), the China Special Funds for Meteorological and Surveying, Mapping and Geoinformation Research in the Public Interest (Project Nos. HY14122136 and GYHY201306055), the National High-Tech Research and Development Program (Project No. 2012AA120905), and the Fund of Shanghai Outstanding Academic Leaders Program (Project No. 12XD1404900).
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Published In
Journal of Surveying Engineering
Volume 141 • Issue 2 • May 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 3, 2012
Accepted: Sep 26, 2014
Published online: Oct 30, 2014
Published in print: May 1, 2015
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