Study on deformation monitoring in mine by DSInSAR based on the phase optimization method under robust M-estimator covariance matrix

The time series Interferometric Synthetic Aperture Radar （InSAR） cannot identify effective monitoring point information on natural surface features such as cultivated land and bare land in the mining area, resulting in insufficient surface deformation information and difficulty in deformation interpretation. To address these problems, a distributed scatterers InSAR （DSInSAR） method based on robust M-estimator covariance matrix eigenvalue decomposition is proposed, and the surface time series deformation of Xiaoyun Coal Mine in 2022 is obtained based on 34 Sentinel-1A images. Firstly, a sample covariance matrix based on the M-estimator is derived to improve robustness to sample outliers and heterogeneous pixels. Then, phase optimization processing based on eigenvalue decomposition for this robust M-estimator covariance matrix is performed, and the similarity between the above optimization model and the general phase optimization model is also analyzed. The deformation information is finally obtained by interpreting the phase information based on the optimized estimated phase. The experimental results show that the DSInSAR based on robust M-estimator covariance matrix eigenvalue decomposition phase optimization increased by about 11.4 times and 0.2 times in monitoring point density compared to conventional SBAS and DSInSAR based on maximum likelihood estimator covariance matrix, respectively, and has the smallest root mean square error, about 22 mm, compared to level data. In addition, the Xiaoyun Coal Mine consists of three main deformation fields, and the time series variation of surface subsidence shows a significant nonlinear trend. And the maximum subsidence in line of sight of the surface in the coal mine is about 418 mm. The research results provide important data support for the inversion of surface deformation rules and disaster prevention and control in mining areas.