Robust Weighted Total Least Squares Algorithm for Three-Dimensional Coordinate Transformation
Abstract Based on the existing weighted symmetric similarity transformation, only the case where the observation value contains random error is considered, and the case where the observation value contains the gross error is not considered. This paper further verifies that the weighted symmetric similarity transformation is not robust. Based on the weighted symmetric similarity transformation, the method of selecting weight iteration is adopted to make the robust weighted symmetric similarity transformation. The model obtains unit weight mean square error with robustness by the median method and utilizes the standardized residual to construct the weight factor function, to obtain a reliable parametric solution. Comparative analysis shows that: when the observations contain 4-6 gross errors, the method of this paper can be used to detect more data that may have gross errors, the weighting factors given are more reasonable, and the obtained parameter solution has higher accuracy and stronger stability.
Key words :
coordinate transformation
total least squares
robust estimation
median method
Cite this article:
WANG Leyang,XU Ranran. Robust Weighted Total Least Squares Algorithm for Three-Dimensional Coordinate Transformation[J]. jgg, 2020, 40(10): 1027-1033.
WANG Leyang,XU Ranran. Robust Weighted Total Least Squares Algorithm for Three-Dimensional Coordinate Transformation[J]. jgg, 2020, 40(10): 1027-1033.
URL:
http://www.jgg09.com/EN/ OR http://www.jgg09.com/EN/Y2020/V40/I10/1027
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DONG Qijia,CHENG Yan,ZHOU Zhonghua,XU Song,QING Yun,WANG Wenjun. Analysis of ITRS to J2000 Coordinate System Conversion Error and Its Influence on Occultation Inversion [J]. jgg, 2021, 41(5): 530-534.
[2]
ZOU Shilin,WU Xing,WANG Fengwei. Regularized Robust Solution for Ill-Posed Weighted Total Least Squares Model [J]. jgg, 2021, 41(11): 1106-1110.
[3]
WU Guangming,LU Tieding. New Methods of Ill-Posed Total Least-Squares with Targeting Singular Value Corrections [J]. jgg, 2019, 39(8): 856-862.
[4]
WANG Leyang,ZOU Chuanyi,WU Lulu. The WHP Quasi Newton Correction Method for Inequality Constrained Partial EIV Model and the SUT Method for Its Precision Estimation [J]. jgg, 2019, 39(6): 648-653.
[5]
JI Kunpu. A Regularized Solution and Accuracy Evaluation of Ill-PosedTotal Least Squares Problem with Equality Constraints [J]. jgg, 2019, 39(12): 1304-1309.
[6]
TAO Wuyong,HUA Xianghong,LU Tieding,CHEN Xijiang,ZHANG Wei. A Total Least Squares Algorithm for Non-Equidistant GM(1,1) Model and Its Ill-Posed Problem [J]. jgg, 2019, 39(1): 45-50.
[7]
PU Lun,TANG Shihua,ZHANG Ziping,HU Xinkai,XIAO Yan. Application of Multi-Quadric Function Based on Ant Colony Algorithm in GPS Elevation Fitting [J]. jgg, 2019, 39(1): 31-35.
[8]
XIAO Zhaobing,SONG Yingchun,XIE Xuemei. Application of a Method for Obtaining Uncertainty in Dislocation Model [J]. jgg, 2018, 38(8): 857-861.
[9]
MA Xiaping,LIN Chaocai, SHI Yun. Research on Coordinate Transformation Method Introducing Datum Rotation Center [J]. jgg, 2018, 38(3): 310-314.
[10]
CHEN Yang,WEN Hongyan,QIN Hui,WANG Qingtao,ZHOU Lü. Robust Total Least Squares Estimated in GM(1,1) for High-Speed Railway Foundation Deformation Prediction [J]. jgg, 2018, 38(2): 140-146.
[11]
WANG Zhu’an,CHEN Yi,MAO Pengyu. The Application of the Posterior Estimation on Weighted Total Least-Squares to Three Dimensional-Datum Transformation [J]. jgg, 2018, 38(2): 216-220.
[12]
QIU Dechao, LU Tieding, DENG Xiaoyuan. A Circular Curve Fitting Solution Based on Partial EIV Model [J]. jgg, 2018, 38(11): 1191-1195.
[13]
QIU Dechao,LU Tieding,MAO Wenfei,WU Guangming. Model and Solution of PEIV Model for Spatial Straight Line Fitting [J]. jgg, 2018, 38(10): 1058-1062.
[14]
TAO Wuyong,LU Tieding,WU Fei,LI Ding. An Improved Total Least Squares Algorithm for Solving Sphere Surface Fitting [J]. jgg, 2018, 38(1): 92-96.
[15]
LI Mingfeng,LIU Zhiliang,WANG Yongming,SUN Xiaorong. Study on an Improved Model for Ill-Conditioned Three-Dimensional Coordinate Transformation with Big Rotation Angles [J]. jgg, 2017, 37(5): 441-445.