病态总体最小二乘问题的广义正则化  

Generalized Regularization to Ill-posed Total Least Squares Problem

作　　者：葛旭明[1] 伍吉仓[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：《测绘学报》2012年第3期372-377,共6页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(41074019);中美国际合作项目(2010DFB20190)

摘　　要：总体最小二乘(TLS)算法可以视为一个降正则化的过程,对比最小二乘算法,病态总体最小二乘方法的解受系数阵数据误差和观测值误差的影响将更为严重。本文探讨用广义正则化的方法降低病态性对总体最小二乘数值求解的影响,以提高求解结果的稳定性。通过多组算例结果表明,本文采用的广义正则化方法在处理病态总体最小二乘问题上具有明显的优势。Total least squares method is a deregularizing procedure, so the ill-posed problems will be more serious. That means errors in the data are more likely to affect the total least squares solution than the least squares solution. It is proposed using generalized regularization to solve ill-posed problems in total least squares, so as to improve stability of the results. Finally, numerical experiments are carried out to demonstrate the performance and efficiency of the generalized regularization method which have significant advantages in solving ill-posed problems.

关 键 词：病态总体最小二乘 EIV 广义正则化 L曲线 

分 类 号：P207[天文地球—测绘科学与技术]