ABSTRACT For the small baseline subset (SBAS) interferometric synthetic aperture radar (InSAR) technique, the construction and subsequent robust solution of a deformation model is a key factor in obtaining monitored surface deformation results with high precision and high reliability. Here, the performance of the least squares (LS) and singular value decomposition (SVD) methods for the robust solution of SBAS InSAR deformation models are compared via tests with simulation and real SAR data. The LS method is used to solve the SBAS InSAR deformation models of 62 and 48 multi-temporal differential interferogram series; the SVD method is used to solve the SBAS InSAR deformation models of 60, 41, 58 and 53 multi-temporal differential interferogram series; the solved deformation results of the six series by the LS and SVD methods are compared and verified with the simulated deformation values and global positioning system (GPS) measurements. The results indicate that there is a moderate ill-posed degree in solving the SBAS InSAR deformation model by the LS method. The LS method can correctly retrieve the deformation information without considering any errors; however, in the case of serious random error, the deformation information acquired through the LS method is different from that of the simulation and is affected by the error of the multi-temporal differential interferometric phase series. The LS-solved results of real SAR datasets of two series are consistent, but are not in good agreement with the results of five GPS measurements. When the number of subsets is two, all types of deformation information solved by the SVD method follow the same rules as the results solved by the LS method. However, when the number of subsets increases to three and four, the stability of the SVD method becomes very poor; the SVD method can then only correctly solve the distribution of deformation in the study area, and the other solved deformation information, such as deformation velocity, is no longer credible.

中文翻译：

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用于 SBAS InSAR 变形模型解的 LS 和 SVD 方法的性能

摘要 对于小基线子集 (SBAS) 干涉合成孔径雷达 (InSAR) 技术，变形模型的构建和后续稳健求解是获得高精度和高可靠性监测表面变形结果的关键因素。在这里，通过对仿真和真实 SAR 数据的测试，比较了最小二乘法 (LS) 和奇异值分解 (SVD) 方法在 SBAS InSAR 变形模型的稳健求解方面的性能。LS方法用于求解62和48多时相微分干涉图系列的SBAS InSAR变形模型；采用SVD方法求解60、41、58、53多时相微分干涉图系列的SBAS InSAR变形模型；用LS和SVD方法求解的六个系列的变形结果与模拟变形值和全球定位系统（GPS）测量值进行了比较和验证。结果表明，LS方法求解SBAS InSAR变形模型存在中等不适定度。LS方法可以在不考虑任何误差的情况下正确检索变形信息；然而，在随机误差严重的情况下，通过LS方法获取的变形信息与模拟不同，受多时相微分干涉相位序列误差的影响。两个系列的真实SAR数据集的LS求解结果是一致的，但与五次GPS测量的结果不一致。当子集数为二时，SVD 方法求解的所有类型的变形信息都遵循与 LS 方法求解的结果相同的规则。但是，当子集数量增加到三个和四个时，SVD方法的稳定性变得很差；SVD 方法只能正确求解研究区内的变形分布，其他求解的变形信息，如变形速度等不再可信。