A joint M-estimation and bayesian estimation method for DS-InSAR deformation estimation

Objectives: Distributed scatterers interferometry (DS-InSAR) significantly increases the number of coherent target pixels in non-urban areas without losing spatial resolution. However, there remains a challenge in balancing the quantity of coherent targets with the accuracy of deformation estimation in conventional DS-InSAR method. To address this issue, we propose a new DS-InSAR method that integrates M-estimation and Bayesian estimation (MB-InSAR). Methods: The method proposes a three-arc strategy to construct the Persistent Scatterer-Disctributed Scatterer (PS-DS) arcs network, which provides a more accurate prior distribution for the DS estimator. Subsequently, the DS points are divided into different categories based on interpolation errors through the velocity interpolation variance. The points with small interpolation errors are solved based on weighted Bayesian estimation, while the remains with large interpolation error are solved based on M-estimation. Results: Applications on simulated datasets demonstrate that MB-InSAR improves the accuracy of long time series velocity estimation by 47%, compared with traditional maximum likelihood estimation and Bayesian estimation. Moreover, MB-InSAR exhibits less sensitivity to PS density and noise. The experiment in Katy and Sienna, Houston, indicated that the MB-InSAR method increased the number of measurement points by 160% and 125%, respectively. Futhermore, the velocity obtained by the MB-InSAR method shows strong consistency with GPS observation, and the maximum difference between the MB-InSAR method and GPS is less than 2.5 mm/a. Conclusions: The MB-InSAR method is effective in improving the estimation accuracy for the DS targets, which can shed more lights in deciphering the fine-scale deformation characteristics with the complex surface environment.