A simplex search algorithm for the optimal weight of common point of 3D coordinate transformation

• Main Authors: GUO Yinggang, LI Zongchun, HE Hua, WANG Zhiying
• Format: Article
• Language: zho
• Published: Surveying and Mapping Press 2020-08-01
• Series: Acta Geodaetica et Cartographica Sinica
• Subjects: common-point-weighted coordinate transformation; optimization algorithm; simplex direct search algorithm; positional coordinate residual; robust estimation
• Online Access: http://html.rhhz.net/CHXB/html/2020-8-1004.htm
• ISSN: 1001-1595; 1001-1595

In order to improve the calculation quality of 3D coordinate transformation parameters, a robust method for weighted-common-point coordinate transformation method is proposed based on optimization algorithm. The minimum sum of weighted squared coordinate residual, which is the coordinate difference from the transferred coordinates to the known coordinates of common points, is taken as the objective function, and the Nelder-Mead simplex direct search algorithm is utilized to search the optimal weights combination of common points coordinates automatically in calculating coordinate transformation parameters. Taking the alignment and installation of particle accelerator magnets as a typical application scenario, simulated data and measured data are used to verify the proposed method. The results show that the algorithm can effectively reduce the weight of gross errors and poor-quality observations. Compared with the least square method and robust method, the sum of weighted squared coordinate residual of the proposed method is smaller, and the quality of coordinate transformation parameters is better. The proposed method can improve the solution quality of 3D coordinate transformation parameters, and is especially applicable to the situation that the priori precision is unknown and the quality of observation is poor.