Background Ionosphere Effects on Geosynchronous SAR Focusing: Theoretical Analysis and Verification Based on the BeiDou Navigation Satellite System (BDS)

Due to the ultra-long aperture time and large coverage characteristics of geosynchronous synthetic aperture radar (GEO SAR), the ionosphere freezing model in the traditional low earth orbit synthetic aperture radar (LEO SAR) imaging is assumed to fail in the GEO SAR, thus it should take the effects of the temporal-spatial variation (TSV) background ionosphere on the GEO SAR imaging into account. Meanwhile, owing to the curved trajectory effects caused by the ultra-long synthetic aperture time of GEO SAR, and the complex geometric kinematic relations between the GEO SAR satellite and the Earth's rotation, the LEO SAR ionospheric effect analysis method based on the traditional kinematic model will be no longer suited to GEO SAR. Moreover, as there are no GEO SAR satellites operating in orbit, how to obtain the real-time ionospheric TEC values on the signal propagation path of GEO SAR satellite has become a great challenge. In this paper, through the establishment of a curved trajectory GEO SAR signal model for long aperture time under the influence of TSV background ionosphere, it has first derived the two-dimensional (2-D) spectrum of GEO SAR signal in the context of background ionosphere, and probed into the GEO SAR 2-D image shift and image defocusing phenomena caused by the background ionosphere, as well as analyzed and summarized the boundary conditions of relevant effects. Concurrently, this paper proposed an approach to equivalently retrieve TEC values on the GEO SAR propagation path based on the BeiDou Navigation Satellite System (BDS) IGSO satellites and combined with the Klobuchar model, which was utilized to equivalently acquire the GEO SAR ionospheric TEC retrieved data. In addition, the retrieved data were used to perform the GEO SAR imaging simulation in the context of the background ionosphere, and verified the correctness of the proposed analysis method.