大旋转角坐标变换非迭代公式  

Non-iterative solution applied to large rotation angle for datum transformation

作　　者：边少锋[1] 李忠美[1] 纪兵[1] 金立新 

机构地区：[1]海军工程大学导航工程系,武汉430033 [2]甘肃铁道综合工程勘察院有限公司,兰州730000 [3]中铁第一勘察设计院集团有限公司,西安710043

出　　处：《测绘科学》2017年第9期43-48,共6页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(41604010;41471387;41574009)

摘　　要：针对求解7参数的过程中,经典的线性化最小二乘法因需线性化、迭代及初值以及存在算法耗时出现不收敛现象的问题,该文对无须迭代的7参数坐标变换公式进行了研究。为避免各类参数间的相关性,采用消去法并按照依次求解旋转参数、比例系数和平移参数的顺序解得坐标变换参数。先利用最小二乘法求解旋转参数,然后通过构建目标函数的方式求解比例系数与平移参数,最终得到无须线性化、无须迭代、无须初值的,可用于大旋转角的7参数坐标变换公式。与线性化最小二乘方法进行相比,该方法具有相当的精度及更高的运算效率,可在一定程度上丰富坐标变换理论。Aiming at the problem that classical linear least squares estimation method requires linear- ization, iteration, and initial values to determine the above-mentioned parameters, which is not only time-consuming but also leads to no convergence; non-iterative solution for seven-parameter datum trans- formation is studied in this paper. An elimination method was introduced to avoid dependency among the different types of parameters, and the seven parameters were determined in the proper order： rotation matrix first, scale factor second, and translation parameters third. Specifically, based on least squares method, the rotation parameters were obtained. Further, to determine the scale factor and translation pa- rameters, an objective function was constructed and its extreme point was found. Finally, a simple solu- tion for datum transformation that did not require linearization, iteration, or initial values was imple- mented, which could be used for coordinate transformation with large rotation angles. Numerical examples show that the proposed method is comparable to the classical linearized least squares method in terms of accuracy, and woks much faster than LS method, which could enrich datum transformation theory to some degree.

关 键 词：坐标变换 7参数 非线性化 非迭代 大旋转角 斜对称矩阵 目标函数 

分 类 号：P228[天文地球—大地测量学与测量工程]