空间直线拟合的混合最小二乘法

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英文篇名：Hybrid total least squares for fitting spatial straight lines 作者：徐文 ; 李建为 ; 张浩 英文作者：Xu Wen;Li Jianwei;Zhang Hao;Guangzhou Urban Planning & Design Survey Research Insitute; 关键词：空间直线 ; 整体最小二乘 ; 混合最小二乘 ; 拟合 ; QR分解 英文关键词：spatial straight line;;total least squares;;hybrid total least squares;;fitting;;QR decomposition 中文刊名：GCKC 英文刊名：Geotechnical Investigation & Surveying 机构：广州市城市规划勘测设计研究院; 出版日期：2019-01-01 出版单位：工程勘察 年：2019 期：v.47;No.354 语种：中文; 页：GCKC201901014 页数：4 CN：01 ISSN：11-2025/TU 分类号：74-77

摘要

在空间直线拟合中传统的最小二乘一般并没有考虑系数矩阵的误差,而整体最小二乘认为其都存在误差,但是实际上系数矩阵中只有一部分有误差。所以就需要引进一种新的算法来充分考虑所有的情况。本文对空间直线方程进行变换,将6参数转换为4参数,使其变成大家熟悉的误差方程,先后用模拟数据以及实测数据用最小二乘、整体最小二乘和混合最小二乘的方法进行处理,计算出累计距离和直线度,得到混合最小二乘比整体最小二乘和最小二乘的解好的结论。所以在空间直线拟合中混合最小二乘方法比整体最小二乘方法考虑的更加全面,得到的解更加可靠。
        Fitting a straight line in three-dimensional space, we generally do not consider the errors in coefficients matrix using the least squares, while we think that the all data of the coefficients matrix including errors using the total least squares. But there is only a part of data include errors, so we need to introduce a new algorithm to fully consider all the circumstances. In this paper, the number of parameters is decreased from six to four to make the equation into a familiar error equation. The simulated data and the measured data are calculated by least squares, total squares and hybrid total least squares. Simultaneous calculation of the cumulative distance and the straightness shows that the solution of the hybrid total least squares is better than the solutions of total squares and least squares. Therefore, the method of hybrid total least squares in spatial linear fitting is more comprehensive than the total least squares method, and the solution obtained is more reliable.

引文

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