Optimal algorithm for distributed scatterer InSAR phase estimation based on cross-correlation complex coherence matrix

Low scattering terrain areas introduce complex phase interference, which reduces the accuracy of deformation signal estimation in InSAR(Interferometric Synthetic Aperture Radar) techniques. Existing covariance matrix-based InSAR phase calculation methods often fail to account for translational offset relations between scatterers leading to inaccuracies, and pixels with zero spatial coherence exist. To address this issue, this paper proposes a distributed scatterer InSAR phase estimation method based on the Cross-Correlation complex coherence matrix. The effectiveness and superiority of the algorithm are verified through simulation and actual data. The results show that: (i) The simulation analysis shows that, compared to the traditional covariance matrix method, the optimal Cross-Correlation matrix improves the interferometric phase, coherence, and accuracy by 21.51%, 15.24%, and 6.52%, respectively. (ii) The actual experimental data show that the interferometric phase optimal by the Cross-Correlation matrix can effectively overcome the pseudo-signal caused by spatial hopping and make the phase more continuous. Compared with the traditional covariance matrix, the average a posteriori coherence and average coherence of arbitrary interference combinations in the Cross-Correlation matrix are improved by 18.12% and 58.10%, respectively. (iii) The number of DS points selected by the Cross-Correlation matrix algorithm is more than that of the covariance matrix algorithm. PS-InSAR (Persistent Scatterer Interferometric Synthetic Aperture Radar) achieved more accurate deformation rates compared to the covariance and correlation matrices, with errors of 9.34, 17.21, and 16.28 $mm\bullet a^{-1}$ when compared against GNSS data, respectively. (iv) The Cross-Correlation matrix reduces the deformation rate error by 5.43 % relative to the covariance matrix. The algorithm provides reliable phase estimation for accurate monitoring of surface deformation in low-scattering regions, supporting geological disaster early warning and resource and environmental management.