Unbiased Estimation of Three-Dimensional Deformation From SAR Interferometry and GNSS Observations

Persistent scatterer interferometry of multitemporal synthetic aperture radar (SAR) satellite images provides deformation along the radar line-of-sight direction. Three-dimensional (3-D) land deformation can be estimated by combining observations from multiple sources and directions, such as multi-temporal SAR images acquired in ascending and descending orbits, with global navigation satellite system (GNSS) data. A bias can be included in the 3-D deformation estimates when the interpolated GNSS data are inconsistent with the actual local deformation. In this study, we propose an optimal method for estimating 3-D land subsidence from SAR images acquired using dual orbits and GNSS data and detecting such bias. It calculates two sets of 3-D ground deformation velocities: one from ascending images and GNSS data and the other from descending images and GNSS data. The subtracted ground deformation velocities have significant values when the interpolated GNSS are inconsistent with ground deformation velocities from SAR observations. We demonstrated the validity using simulated images. In addition, we examined the number of observation equations that had the least effect on the bias. We applied this method to the Kansai International Airport in Japan using advanced land observing satellite 2/phased array type L-band SAR 2 ascending and descending images. We assessed the validity of the observation equation models based on the viewpoints of root mean squared errors and the relative residual error generated in the estimation. We found that when the inconsistency due to the interpolation is available, the optimal model uses four observation variables: two LOS deformation velocities and interpolated East-West and North-South deformation velocities from GNSS observations.