总体最小二乘拟合问题求解方法的比较研究  

Comparison between solutions of Total Least Squares fitting problem

作　　者：龚循强[1,2,3] 刘国祥[1] 李志林[1] 周秀芳[4] 

机构地区：[1]西南交通大学地球科学与环境工程学院,成都611756 [2]江西省数字国土重点实验室(东华理工大学),南昌330013 [3]精密工程与工业测量国家测绘地理信息局重点实验室,武汉430079 [4]四川农业大学经济管理学院,成都611130

出　　处：《测绘科学》2014年第9期29-33,共5页Science of Surveying and Mapping

基　　金：973计划课题(2012CB719901);国家自然科学基金(41201475);江西省数字国土重点实验室开放研究基金资助项目(DLLJ201407);精密工程与工业测量国家测绘地理信息局重点实验室开放基金项目(PF2013-15)

摘　　要：目前对总体最小二乘求解方法的研究,出现了奇异值分解的总体最小二乘法、顾及自变量和因变量误差的总体最小二乘法及正交总体最小二乘法。在模型推导的基础上,本文对3种总体最小二乘法在直线和平面拟合中求解的参数及其精度进行了分析,通过与最小二乘法的比较表明,总体最小二乘法得到的拟合结果更加稳健,且以正交总体最小二乘法的拟合结果为最优。In the current research of Total Least Squares solution methods, singular value decomposi- tion of Total Least Squares, Total Least Squares for taking account of independent and dependent variable errors and orthogonal Total Least Squares are put forward. On the basis of model derivations of Total Least Squares based on different algorithms, the straight line and plane fitting parameters estimation and their precision were analyzed in this paper. The results were compared with Least Squares. It was shown that more robust fitting results could be got by Total Least Squares based on different algorithms. At the same time, the results of orthogonal total least squares would be optimal.

关 键 词：总体最小二乘法 拟合 最小二乘法 奇异值分解 正交总体最小二乘法 

分 类 号：P207.2[天文地球—测绘科学与技术]