一种基于奇异值修正的SBAS-InSAR形变模型正则化解算方法  

A Regularization Method for SBAS-InSAR Deformation Model Based on Singular Value Correction

作　　者：郑丹[1] 林一鸣 翟敏[3] ZHENG Dan;LIN Yiming;ZHAI Min(Heilongjiang Institute of Geomatics Engineering,Harbin 150081,China;The Second Geodetic Surveying Brigade,Ministry of Natural Resources,Harbin 150025,China;College of Geodesy and Geomatics,Shandong University of Science and Technology,Qingdao 266590,China)

机构地区：[1]黑龙江地理信息工程院,黑龙江哈尔滨150081 [2]自然资源部第二大地测量队,黑龙江哈尔滨150025 [3]山东科技大学测绘与空间信息学院,山东青岛266590

出　　处：《测绘与空间地理信息》2021年第S01期263-266,271,共5页Geomatics & Spatial Information Technology

摘　　要：在利用SBAS-InSAR进行地表形变监测中,形变模型的病态性会对反演结果的精度产生影响。Tikhonov正则化方法是通过引入正则化参数及正则化矩阵,将病态问题转换为病态性较弱或良性问题进行解算,其关键是构建起有效的正则化矩阵。本文在奇异值分解正则化矩阵构建方法的基础上,提出了基于最小均方误差奇异值修正的正则化方法,该方法通过比较方差下降量和偏差引入量,确定满足均方误差最小的较小奇异值分界值,进而通过奇异值修正降低估计方差并减少偏差的引入,结合北京地区SBAS-InSAR的沉降反演实验对该方法的有效性进行了验证。In the use of SBAS-InSAR for land subsidence monitoring,the ill-posed of deformation model will affect the accuracy of the inversion results.The Tikhonov regularization method introduces regularization parameter and regularization matrix to improve ill-posed problem,and the key point is to construct the effective regularization matrix.Based on the regularization matrix construction method by singular value decomposition,a singular value correction regularization matrix method of minimum mean square error is proposed.By comparing the reduced variance and introduced bias,the boundary value of the smaller singular value that satisfied minimum mean square error is determined.Then the variance is decreased and the introduced bias is reduced by singular value correction.The effective of this method is verified by SBAS-InSAR deformation inversion experiment in Beijing area.

关 键 词：奇异值修正 SBAS-InSAR 正则化方法 正则化矩阵 最小二乘 

分 类 号：P25[天文地球—测绘科学与技术] TB22[天文地球—大地测量学与测量工程]