Baseline Optimization for Spatial-Temporal Coupling in Geosynchronous Differential Synthetic Aperture Radar Tomography

Differential synthetic aperture radar tomography (D-TomoSAR) uses multiple SAR acquisitions at different times to form an elevation-time 2-D synthetic aperture, enabling recovery of the target's 3-D structure and deformation velocity. However, the imaging performance of D-TomoSAR is influenced by the spatial-temporal baseline distribution, which is one of the crucial factors. Due to the difference in orbit altitude, the effects of various perturbation forces on geosynchronous SAR (GEO SAR) are significantly different from those on low Earth orbit SAR (LEO SAR), leading to different geometries in the spatial-temporal baseline distributions of GEO SAR and LEO SAR in the repeat-pass acquisitions. The spatial-temporal baseline distribution of LEO SAR is random, while that of GEO SAR is coupled. Although GEO SAR obtains a large number of acquisitions due to the short repeat-pass time, using data under all spatial-temporal baselines for D-TomoSAR does not necessarily provide the best imaging results. Therefore, how to select spatial-temporal baselines that can improve the estimation accuracy is important. In this article, the Cramér–Rao lower bound of GEO D-TomoSAR estimation accuracy is determined by considering multiple factors, including baseline decorrelation and spatial-temporal coupling. The optimal spatial-temporal baseline selection is modeled as a multiobjective problem and solved by the Nondominated Sorting Genetic Algorithm II (NSGA-II). Given the absence of in-orbit GEO SAR and the orbital similarity between GEO SAR and BeiDou Inclined Geosynchronous Orbit (IGSO) satellite, the real ephemeris of BeiDou IGSO satellite is used to simulate the baseline distribution of GEO SAR and verify the baseline optimization method.