Adaptive Two-Stage Monte Carlo Algorithm for Accuracy Estimation of Total Least Squares
Publication: Journal of Surveying Engineering
Volume 149, Issue 1
Abstract
The existing theory of the total least squares (TLS) accuracy estimation contains the following problems: (1) the approximation function method based on the Taylor series expansion cannot avoid the derivative operation; (2) the selection of the number of simulations for the Monte Carlo method is subjective; and (3) the adaptive Monte Carlo algorithm is complex. Aiming at these problems, we introduce the adaptive two-stage Monte Carlo (ATMC) algorithm into the theory of accuracy estimation of the TLS. In order to consider the biases of estimation for parameters, residuals, and the estimation of the variance of unit weight, the computing process for accuracy estimation of the TLS contains bias estimation and accuracy estimation, and the algorithm is provided. In addition, based on the quasi-Monte Carlo method, an adaptive two-stage quasi-Monte Carlo (ATQMC) algorithm is proposed for the calculation of the expected bias in parameter estimates, and the algorithm flow is given. The experimental results verified the effectiveness of the ATMC and ATQMC algorithms. Compared with the ATMC algorithm, the ATQMC algorithm proposed in this paper is more efficient in the calculation of the expected bias in parameter estimates.
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Data Availability Statement
Some data, models, or code generated or used during the study are available from the corresponding author by reasonable request. The data (e.g., simulation data for the part of numerical experiments) can be provided by the .mat file.
Acknowledgments
The authors are grateful to all of the anonymous reviewers and editors for their careful review and valuable suggestions, which improved the quality of this paper. This research is supported by the National Natural Science Foundation of China (Nos. 42174011 and 41874001).
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Journal of Surveying Engineering
Volume 149 • Issue 1 • February 2023
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© 2022 American Society of Civil Engineers.
History
Received: Nov 9, 2021
Accepted: Jun 9, 2022
Published online: Sep 16, 2022
Published in print: Feb 1, 2023
Discussion open until: Feb 16, 2023
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- Saeid Gholinejad, Alireza Amiri-Simkooei, Multivariate Weighted Total Least Squares Based on the Standard Least-Squares Theory, Journal of Surveying Engineering, 10.1061/JSUED2.SUENG-1424, 149, 4, (2023).