三维坐标转换公共点最优权值的单纯形搜索算法

为提高三维坐标转换参数的求解质量,本文基于最优化算法提出了一种稳健的公共点加权坐标转换方法。以坐标转换后公共点的点位残差加权平方和最小为目标函数,利用Nelder-Mead单纯形直接搜索算法,寻找公共点坐标分量在解算坐标转换参数时的最优权重组合。以粒子加速器磁铁的准直安装为应用场景,利用模拟数据和实测数据对本文方法进行验证。结果表明:本文方法能够有效降低粗差观测值及质量不佳观测值的权重。与最小二乘、抗差估计等方法相比,本文方法解算结果的点位残差加权平方和更小,坐标转换参数质量更优。本文方法能提高三维坐标转换参数的求解质量,尤其适用于验前精度未知、观测数据质量不佳的情况。

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

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.