短基线集形变模型反演的正则化解算方法

doi:10.11947/j.AGCS.2016.20150143

测绘学报 ›› 2016, Vol. 45 ›› Issue (5): 566-573.doi: 10.11947/j.AGCS.2016.20150143

短基线集形变模型反演的正则化解算方法

姜兆英^1,2, 刘国林¹, 陶秋香¹

1. 山东科技大学测绘科学与工程学院, 山东青岛 266590;
2. 青岛农业大学理学与信息科学学院, 山东青岛 266109

收稿日期:2015-03-17 修回日期:2016-01-04 出版日期:2016-05-20 发布日期:2016-05-30
通讯作者: 刘国林 E-mail:gliu@sdust.edu.cn
作者简介:姜兆英(1981-),女,博士生,研究方向为InSAR数据处理和模型算法。E-mail: 15964287012@163.com
基金资助:
国家自然科学基金(41274007;41404003);山东省自然科学基金(ZR2012DM001);高等学校博士学科点专项科研基金(20123718110001);山东省泰山学者建设工程专项经费(TSXZ201509)

Regularization solution of Small Baseline Subset Deformation Model Inversion

JIANG Zhaoying^1,2, LIU Guolin¹, TAO Qiuxiang¹

1. Geomatics College, Shandong University of Science and Technology, Qingdao 266590, China;
2. College of Science and Information, Qingdao Agricultural University, Qingdao 266109, ChinaAbstract

Received:2015-03-17 Revised:2016-01-04 Online:2016-05-20 Published:2016-05-30
Supported by:
The National Natural Science Foundation of China (Nos. 41274007;41404003);Shandong Province Natural Science Foundation of China (No. ZR2012DM001);Specialized Research Fund for the Doctoral Program of Higher Education (No. 20123718110001);Shandong Taishan Scholar Construction Project under Special Funding (No. TSXZ201509)

摘要/Abstract

摘要： 针对短基线集形变模型反演中法方程系数矩阵呈病态的问题,提出一种正则化稳健解算方法。该方法基于Tikhonov正则化理论,将形变速率求解问题转化为极小化问题,根据L-曲线法选取正则化参数,考虑最小二乘残差各个分量间的关系选取正则化矩阵,实现短基线集形变模型反演的稳健解算。分别采用LS法、岭估计法和Tikhonov正则化法对覆盖北京地区的29景ENVISAT ASAR数据进行处理,反演出研究区沉降速率图。通过对代表不同沉降情况的21个点的均方误差值和时间相干值、整个研究区的均方误差图等的对比分析,表明本文提出的短基线集形变模型反演的正则化稳健解算方法可获取更可靠的形变监测结果。

关键词: 短基线集, 条件数, Tikhonov正则化, 岭估计, 均方误差

Abstract: For the coefficient matrix of the normal equation is ill-conditioned during inverting deformation model of small baseline subset (SBAS) InSAR technique, a regularization robust method is proposed. Based on Tikhonov regularization theory, this method converts the problem of how to solve the deformation rate into minimization problem. According to L-curve method to choose regularization parameter, considering the relationship between the individual components of least-squares residuals to choose regularization matrix, thus it achieves robust solution of SBAS deformation model inversion. We adopt respectively least-squares estimation, ridge estimation and Tikhonov regularization method to deal with 29 ENVISAT ASAR dataset relevant to the Beijing area, achieving the subsidence rate map of the study area. Through comparative analysis among the mean square error (MSE) of 21 points on behalf of the different subsidence, temporal coherence values and MSE maps of the entire study area, we confirm that Tikhonov regularization robust method in inverting SBAS deformation model can obtain more reliable results of deformation monitoring.

Key words: small baseline subset, condition number, Tikhonov regularization, ridge estimation, mean squared error

中图分类号:

P226

姜兆英, 刘国林, 陶秋香. 短基线集形变模型反演的正则化解算方法[J]. 测绘学报, 2016, 45(5): 566-573.

JIANG Zhaoying, LIU Guolin, TAO Qiuxiang. Regularization solution of Small Baseline Subset Deformation Model Inversion[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5): 566-573.

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短基线集形变模型反演的正则化解算方法

Regularization solution of Small Baseline Subset Deformation Model Inversion

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