Second-Order Approximation Function Method for Precision Estimation of Total Least Squares

AbstractTo 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 se...

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Bibliographic Details
Published in:Journal of surveying engineering 2018-02, Vol.145 (1)
Main Authors: Wang, Leyang, Zhao, Yingwen
Format: Article
Language:English
Subjects:
Approximation
Covariance
Economic models
Error correction
Estimates
Least squares
Order parameters
Parameter estimation
Queuing theory
Technical Papers
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Summary:AbstractTo 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.
ISSN:0733-9453
1943-5428
DOI:10.1061/(ASCE)SU.1943-5428.0000266