The performance of LS and SVD methods for SBAS InSAR deformation model solutions

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.