An M-Estimation Method for InSAR Nonlinear Deformation Modeling and Inversion

Satellite synthetic aperture radar interferometry (InSAR) has become a recognized and reliable surface deformation monitoring technology in recent years. However, the complexity of surface deformation, driven by various physical mechanisms, presents itself in different forms such as secular trend, cyclical fluctuations, and irregular variations in time series. Consequently, the limitations of conventional InSAR technology, which relies on linear deformation assumptions, make it challenging to meet the requirements of monitoring complex nonlinear deformation. Additionally, the commonly used parameter inversion method based on the least squares approach is unsuitable for non-Gaussian observation error distribution with gross errors. To address these issues, we propose an InSAR interferometric phase nonlinear function model that considers zero-mean second-order stochastic differential equations and periodic changes. This model can quantitatively describe the law of surface deformation driven by multiple physical factors. Furthermore, we utilize an efficient M-estimation method, known for its high robustness, to optimize the model parameters and mitigate the impact of non-Gaussian noise and/or gross errors in InSAR observation and data processing. By conducting simulation experiments, it verifies that the proposed method is more robust than the conventional InSAR method. Finally, the processing and analysis of Sentinel-1 data in the overlying rock glacier area confirm the effectiveness of the proposed method in extracting nonlinear surface deformation.