病态总体最小二乘靶向奇异值修正法  

New Methods of Ill-Posed Total Least-Squares with Targeting Singular Value Corrections

作　　者：吴光明 鲁铁定[1,2,3] WU Guangming;LU Tieding(Faculty of Geomatics, East China University of Technology, 418 Guanglan Road, Nanchang 330013, China;Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, MNR,418 Guanglan Road, Nanchang 330013, China;Jiangxi Province Key Lab for Digital Land, 418 Guanglan Road, Nanchang 330013, China)

机构地区：[1]东华理工大学测绘工程学院,南昌330013 [2]国家自然资源部流域生态与地理环境监测重点实验室,南昌330013 [3]江西省数字国土重点实验室,南昌330013

出　　处：《大地测量与地球动力学》2019年第8期856-862,共7页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(41374007,41464001);江西省科技落地计划(KJLD12077);江西省教育厅科技项目(GJJ13457);江西省自然科学基金(2017BAB203032);国家重点研发计划(2016YFB0501405,2016YFB0502601-04)~~

摘　　要：一般病态问题是法矩阵出现几个特征奇异值,计算过程中可用靶向矩阵修正奇异值。总体最小二乘迭代过程中,系数矩阵不断微变,靶向矩阵也应随之改变。针对靶向矩阵变化问题,推导2种病态总体最小二乘靶向奇异值修正法,先求出新系数矩阵,再求靶向矩阵,最后迭代计算出参数估值。实验验证了该方法的优势。The general ill-posed problem is that there are several singular eigenvalues in the coefficient matrix, and the singular value can be corrected with the target matrix in the calculation process. In the total least squares iteration process, the coefficient matrix is constantly changing, so the target matrix should also change accordingly. For target matrix changing, this paper deduces two new methods of ill-posed total least-squares targeting singular value corrections. By finding the new coefficient matrix and then finding the target matrix, the iteration is calculated with the parameter estimate and used in the example. The results show that these methods have some advantages.

关 键 词：病态 总体最小二乘 系数矩阵 靶向修正 

分 类 号：P207[天文地球—测绘科学与技术]