大旋转角坐标变换非迭代公式

发布时间：2018-02-22 00:48

本文关键词： 坐标变换参数非线性化非迭代大旋转角斜对称矩阵目标函数　出处：《测绘科学》2017年09期 　论文类型：期刊论文

【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。
[Abstract]:In order to solve the problem of solving 7 parameters, the classical linearized least square method needs linearization, iteration and initial value, and the time consuming of the algorithm does not converge. In this paper, the formula of coordinate transformation of 7 parameters without iteration is studied. In order to avoid the correlation between various parameters, the elimination method is adopted and the rotational parameters are solved in turn. The coordinate transformation parameters are obtained by the sequential solution of the proportional coefficient and the translation parameter. First, the rotation parameters are solved by the least square method, and then the proportional coefficient and the translation parameter are solved by constructing the objective function, and the result is that there is no need for linearization and iteration. It can be used for the 7-parameter coordinate transformation formula of large rotation angle without initial value. Compared with the linearized least square method, this method has considerable accuracy and higher operational efficiency, and can enrich the coordinate transformation theory to a certain extent.
【作者单位】：海军工程大学导航工程系;甘肃铁道综合工程勘察院有限公司;中铁第一勘察设计院集团有限公司;
【基金】：国家自然科学基金项目(41604010,41471387,41574009)
【分类号】：P226.3

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