基于信噪比检验的病态总体最小二乘谱修正迭代法  

Iteration Method of Correcting Characteristic Value to Ill-Posed Total Least Squares Based on Signal-to-Noise Ratio

作　　者：郭杰 郭淑妹 张宁 GUO Jie;GUO Shu-mei;ZHANG Ning(Institute of Science,Information Engineering University,Zhengzhou 450001,China)

机构地区：[1]信息工程大学基础部,郑州450001

出　　处：《西南师范大学学报（自然科学版）》2020年第3期10-15,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(41174005,41474009).

摘　　要：针对病态总体最小二乘谱修正迭代算法的不足,基于复共线性综合诊断,合理判断参数估计是否受到复共线性危害及危害程度,然后制定精准的正则化策略,提出了基于信噪比检验的病态总体最小二乘谱修正迭代算法,根据信噪比检验结果确定谱修正矩阵,根据改造的L曲线法确定谱修正参数.最后通过模拟算例验证了该算法求解病态总体最小二乘问题的数值稳定性和有效性.In this paper,the iteration method of correcting characteristic value and its improved algorithm have been analyzed in the detail,combined with its feature and shortcomings.Then the iteration method by correcting characteristic values to ill-posed total least squares based on signal-to-noise ratio been proposed.At last,some simulated examples been investigated to verify the numerical stability and effectiveness of parameter estimation of the proposed method.

关 键 词：总体最小二乘 病态模型 谱修正迭代 复共线性 信噪比 

分 类 号：P207[天文地球—测绘科学与技术]