Second-Order Approximation Function Method for Precision Estimation of Total Least Squares
Publication: Journal of Surveying Engineering
Volume 145, Issue 1
Abstract
To obtain more accurate formulas for precision estimation and to continue work on the adjustment of total least squares (TLS), the second-order approximation function method for the precision estimation of the TLS adjustment was investigated. According to least-squares (LS) criterion, the second-order Taylor expansions between parameter estimates or corrections and observational errors were derived. By the error propagation law, the formulas for biases in parameter estimates and residuals and the second-order approximate covariance and mean squared error matrices for the parameter estimates were obtained. Then, the implementation process of the second-order approximation function method for precision estimation was also designed. Results of the examples showed that the second-order approximation function method could effectively calculate biases and covariance or mean squared error matrices for precision estimation. The second-order approximation function method can provide more precision information for judging the qualities of parameter estimates and the nonlinear degree of the function model, contributing, in part, to the integrity of the theory on precision estimation of the TLS adjustment.
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Acknowledgments
The authors are grateful to the anonymous reviewers and editors for their valuable comments, which were used to improve the quality of this paper. This research was supported by the National Natural Science Foundation of China (Grants 41664001 and 41874001), Support Program for Outstanding Youth Talents in Jiangxi Province (Grant 20162BCB23050), and National Key Research and Development Program (Grant 2016YFB0501405).
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Published In
Journal of Surveying Engineering
Volume 145 • Issue 1 • February 2019
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Dec 19, 2017
Accepted: Jun 15, 2018
Published online: Oct 11, 2018
Published in print: Feb 1, 2019
Discussion open until: Mar 11, 2019
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