空间直线拟合的整体最小二乘算法

姚宜斌; 黄书华; 孔建; 何军泉

doi:10.13203/j.whugis20120104

空间直线拟合的整体最小二乘算法

¹ 武汉大学测绘学院,湖北武汉,430079;² 俄亥俄州立大学地球科学学院,美国哥伦布,43210;³ 温州市勘察测绘研究院,浙江温州,325000

基金项目: 国家自然科学基金资助项目(41174012,41274022)；国家863计划资助项目(2013AA122502)；教育部新世纪优秀人才支持计划资助项目(NCET-12-0428)

详细信息

作者简介:
姚宜斌,教授,博士生导师,现主要从事测量数据处理基础理论与方法研究。

中图分类号: P207.2
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出版历程
- 收稿日期: 2013-02-25
- 修回日期: 2014-05-04
- 发布日期: 2014-05-04

)Total Least Squares Algorithm for Fitting Spatial Straight Lines

¹School of Geodesy and Geomatics,Wuhan University,Wuhan 430079,China;²Ohio State University School of Earth Science,Columbus,OH 43210,USA;³Reconnaissance Mapping Research Institute of Wenzhou,Wenzhou 32500,China

Funds: The National Natural Science Foundation of China,Nos.41174012,41274022;the National 863Program,No.2013AA122502;New Century Excellent Talents in University,No.NCET-12-0428.

More Information

Author Bio:
YAO Yibin,professor,PhD supervisor,specializes in measurement data processing theory and methods.

摘要

摘要: 目的提出了一种基于整体最小二乘的空间直线拟合方法。首先,对空间直线的标准式方程进行变换,并附加参数转换的过程,将6个参数简化为4个;然后,将方程改写为矩阵形式,由此巧妙地将空间直线拟合的问题转化为整体最小二乘的参数求解问题,利用TLS迭代法求得转换后的空间直线拟合的4个参数,再通过参数回代的方法恢复空间直线的6个基本参数。通过算例比较验证了该方法的可行性和有效性。
- 空间直线 /
- 整体最小二乘 /
- SVD /
- 拟合
Abstract: Objective To address the problem of fitting a straight line in three-dimensional space,since the equa-tion is a six parameter equation,not a simple linear relationship,the traditional least squares methodcannot be used to solve it.In this paper,a new method of space line based on the total least squares isproposed.Firstly,the number of parameters was decreased from six to four by changing the standardequation of the straight line,then re-expressed the equation in the form of a matrix.Therefore,thefitting problem was transformed to the parameter-solving problem in total least squares.Further,thefitting four parameters were obtained using a TLS iteration,and the six parameters of the space lineswere recovered through a backtracking method.An experiment in the paper verifies the effectivenessand applicability of the new method.
- spatial straight line /
- TLS /
- SVD /
- fitting