Robust Solution for Coordinate Transformation Based on Coordinate Component Weighting
Publication: Journal of Surveying Engineering
Volume 149, Issue 3
Abstract
This study proposed classifying and weighting the coordinate components to improve the precision of the coordinate transformation. A coordinate transformation model should avoid the participation of angle parameters to reduce the error caused by the linearization process when describing the rotation matrix. Based on Rodrigues’ formula, the coordinate transformation model and the calculation method for the initial values of the parameters were given. It is difficult to reasonably determine the pretest information for robust estimation, so the median function was used to classify and estimate the error in the coordinate components to determine the threshold value of the weight function in each direction. The third scheme of the Institute of Geodesy and Geophysics (IGG3) weight function was used as the equivalent weight function. The parametric adjustment method with additional constraints was adopted to solve the transformation parameters. The simulation test and case analysis were conducted using the tunnel control network of particle accelerator engineering as an example. The results show that the method in this study is not affected by empirical parameters when determining the weight, its robustness is stronger than the traditional robust estimation method, and the coordinate transformation precision is higher.
Formats available
You can view the full content in the following formats:
Data Availability Statement
All data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The writers thank the anonymous reviewers and the editor for their valuable comments on the manuscript. The work described in this paper was substantially supported by the National Natural Science Foundation of China (Project No. 41974216). The authors are grateful to engineer Zhao Wenbin for providing the data required for the research.
References
Chen, Y., Y. Shen, and D. Liu. 2004. “A simplified model of three dimensional-datum transformation adapted to big rotation angle.” Geomatics Inf. Sci. Wuhan Univ. 29 (12): 1101–1105.
Eshagh, M., L. Sjöberg, and R. Kiamehr. 2007. “Evaluation of robust techniques in suppressing the impact of outliers in a deformation monitoring network—A case study on the Tehran Milad tower network.” Acta Geod. Geophys. Hung. 42 (4): 449–463. https://doi.org/10.1556/AGeod.42.2007.4.6.
Fang, X., L. Huang, and W. Zeng. 2018. “On an improved iterative reweighted least squares algorithm in robust estimation.” Acta Geod. Cartographica Sin. 47 (10): 1301–1306. https://doi.org/10.11947/j.AGCS.2018.20170576.
Felus, F., and R. Burtch. 2009. “On symmetrical three-dimensional datum conversion.” GPS Solut. 13 (1): 65–74. https://doi.org/10.1007/s10291-008-0100-5.
Grafarend, E. W., and J. Awange. 2003. “Nonlinear analysis of the three-dimensional datum transformation.” J. Geod. 77 (1–2): 66–76. https://doi.org/10.1007/s00190-002-0299-9.
Greenfeld, S. 1997. “Least squares weighted coordinate transformation formulas and their applications.” J. Surv. Eng. 123 (4): 147–161. https://doi.org/10.1061/(ASCE)0733-9453(1997)123:4(147).
Guo, Y., Z. Li, and H. He. 2020. “A simplex search algorithm for the optimal weight of common point of 3d coordinate transformation.” Acta Geod. Cartographica Sin. 49 (8): 1004–1013. https://doi.org/10.11947/j.AGCS.2020.20190409.
Jazar, R. N. 2007. Theory of applied robotics: Kinematics, dynamics, and control. New York: Springer.
Li, D., and X. Yuan. 2002. Error processing and reliability theory. Wuhan: Wuhan University Press.
Liu, C., B. Wang, and X. Zhao. 2018. “Three-dimensional coordinate transformation model and its robust estimation method under Gauss-Helmert model.” Geomatics Inf. Sci. Wuhan Univ. 43 (9): 1320–1327. https://doi.org/10.13203/j.whugis20160348.
Lu, J., Y. Chen, B. Li, and X. Fang. 2014. “Robust total least squares with reweighting iteration for three-dimensional similarity transformation.” Surv. Rev. 46 (334): 28–36. https://doi.org/10.1179/1752270613Y.0000000050.
Lv, Z., J. Wu, and Y. Gong. 2016. “Improvement of a three-dimensional coordinate transformation model adapted to big rotation angle based on quaternion.” Geomatics Inf. Sci. Wuhan Univ. 41 (4): 547–553. https://doi.org/10.13203/j.whugis20140171.
Tao, Y., J. Gao, and Y. Yao. 2016. “Solution for robust total least squares estimation based on median method.” Acta Geod. Cartographica Sin. 45 (3): 297–301. https://doi.org/10.11947/j.AGCS.2016.20150234.
Uygur, S. O., O. Akyilmaz, and C. Aydin. 2021. “Solution of nine-parameter affine transformation based on quaternions.” J. Surv. Eng. 147 (3): 04021011. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000364.
Wu, Z., W. Luo, and J. Li. 2014. “On position of gross errors of common points in coordinate transformation and reducing influence of gross errors.” J. Geod. Geodyn. 34 (1): 118–122. https://doi.org/10.14075/j.jgg.2014.01.011.
Xu, B., J. Gao, and Z. Li. 2015. “The application of the total least squares algorithm based on reweighting iteration to the three-dimensional coordinates.” J. Geod. Geodyn. 35 (4): 693–696. https://doi.org/10.14075/j.jgg.2015.04.033.
Yang, L., and Y. Shen. 2020. “Robust M estimation for 3D correlated vector observations based on modified bifactor weight reduction model.” J. Geod. 94 (3): 1–17. https://doi.org/10.1007/s00190-020-01351-1.
Yang, Y. 1994. “Robust estimation for dependent observations.” Manuscr Geod. 19 (1): 10–17.
Yao, J., B. Han, and Y. Yang. 2006. “Applications of lodrigues matrix in 3d coordinate transformation.” Geomatics Inf. Sci. Wuhan Univ. 31 (12): 1094–1096.
Yu, G., G. Feng, and J. Zhang. 2018. “Discussion on plane coordinate transformation based on barycentre datum.” GNSS World China 43 (1): 15–18. https://doi.org/10.13442/j.gnss.1008-9268.2018.01.003.
Zeng, W., and B. Tao. 2003. “Non-linear adjustment model of three-dimensional coordinate transformation.” Geomatics Inf. Sci. Wuhan Univ. 28 (5): 566–568.
Zhou, J., Y. Huang, and Y. Yang. 1997. Robust least squares. Wuhan: Huazhong University of Science and Technology Press.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 149 • Issue 3 • August 2023
Copyright
This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.
History
Received: Aug 24, 2022
Accepted: Feb 7, 2023
Published online: Apr 10, 2023
Published in print: Aug 1, 2023
Discussion open until: Sep 10, 2023
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.