顾及粗差的混合最小二乘平差实验分析  

Mixed Total Least Squares and Least Squares Adjustment Experimental Anal Ysis With Gross Error Considered

作　　者：张海华[1] 刘春[1,2] 

机构地区：[1]同济大学测量与国土信息工程系,上海200092 [2]现代工程测量国家测绘局重点实验室,上海200092

出　　处：《现代测绘》2010年第5期8-12,共5页Modern Surveying and Mapping

基　　金：上海市教育委员会科研创新项目(课题号:10ZZ25);海岛礁国家测绘局重点实验室开放基金项目(课题号:2009B10)资助

摘　　要：通过详细介绍总体最小二乘法以及其与经典最小二乘法的关系,引出综合了经典最小二乘法与总体最小二乘法的混合最小二乘平差法。为了研究混合最小二乘法的优劣,本文设计一套比较混合最小二乘法与经典最小二乘法的实验方案。通过实验结果可知,混合最小二乘法并非总优于经典最小二乘法,只有当系数阵误差比观测值误差大或略小时,混合最小二乘法才始终优于经典最小二乘法。With the help of the detailed description of the total least squares（TLS for short） method and its relationship with classical least squares（LS for short） method,the mixed total least squares and least squares（TLS-LS for short） method has been introduced to study its application effects and scopes.Mixed TLS-LS combines the features of LS and TLS.In order to study the mixed TLS-LS method,this paper has been designed a set of experiment scheme with comparing TLS-LS method and LS method.Numerical results show that the mixed TLS-LS method is not always superior to the LS method.Only when the error of coefficient matrix larger or slightly smaller than the error of observation matrix,mixed TLS-LS method is better than LS method.

关 键 词：经典最小二乘 总体最小二乘 混合最小二乘 平差 

分 类 号：P207[天文地球—测绘科学与技术]