一种构造正则化矩阵的新方法  

A New Method of Constructing Regularized Matrix

作　　者：吴光明 鲁铁定[1,2,3] 邓小渊 邱德超[1] WU Guangming;LU Tieding;DENG Xiaoyuan;QIU Dechao(Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASMG,Nanchang 330013, China;Key Lab for Digital Land and Resources of Jiangxi Province, Nanchang 330013, China;Geomatics Center of Zhejiang Province, Hangzhou 310012, China)

机构地区：[1]东华理工大学测绘工程学院,南昌市广兰大道418号330013 [2]流域生态与地理环境监测国家测绘地理信息局重点实验室,南昌市广兰大道418号330013 [3]江西省数字国土重点实验室,南昌市广兰大道418号330013 [4]浙江省地理信息中心,杭州市保俶北路83号310012

出　　处：《大地测量与地球动力学》2019年第1期61-65,共5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：在系数矩阵病态时进行参数求解,合理地选择正则化参数和正则化矩阵可以提高参数估计的可靠性。针对正则化矩阵如何构造的问题,提出一种新的正则化矩阵构造方法。通过法矩阵较小奇异值对应的特征向量构造出一个对称矩阵,用该矩阵的主对角线元素构造出对角矩阵,然后与单位矩阵组合得出一种新的正则化矩阵。实验表明,当正则化参数小于1时,新算法的参数估值优于岭估计。In parameter solving under the conditions of coefficient matrix,the rational selection of regularization parameters and regularization matrix can improve the reliability of parameter estimation.The symmetric matrix is constructed by the eigenvectors corresponding to the smaller singular values of the matrix.The diagonal matrix is constructed by the main diagonal elements of the matrix,and then a new regularization matrix is obtained by combining with the unit matrix.The experimental results show that when the regularization parameter is less than1,the parameter estimation of this algorithm is better than the ridge estimation.

关 键 词：系数矩阵 正则化矩阵 奇异值 均方误差 岭估计 

分 类 号：P207[天文地球—测绘科学与技术]