Ground penetrating radar mounted on a small unmanned aerial vehicle (UAV) is a promising tool to assist humanitarian landmine clearance. However, the quality of synthetic aperture radar images depends on accurate and precise motion estimation of the radar antennas as well as generating informative viewpoints with the UAV. This paper presents a complete and automatic airborne ground-penetrating synthetic aperture radar (GPSAR) system. The system consists of a spatially calibrated and temporally synchronized industrial grade sensor suite that enables navigation above ground level, radar imaging, and optical imaging. A custom mission planning framework allows generation and automatic execution of stripmap and circular GPSAR trajectories controlled above ground level as well as aerial imaging survey flights. A factor graph based state estimator fuses measurements from dual receiver real-time kinematic (RTK) global navigation satellite system (GNSS) and an inertial measurement unit (IMU) to obtain precise, high rate platform positions and orientations. Ground truth experiments showed sensor timing as accurate as 0.8 {\mu}s and as precise as 0.1 {\mu}s with localization rates of 1 kHz. The dual position factor formulation improves online localization accuracy up to 40 % and batch localization accuracy up to 59 % compared to a single position factor with uncertain heading initialization. Our field trials validated a localization accuracy and precision that enables coherent radar measurement addition and detection of radar targets buried in sand. This validates the potential as an aerial landmine detection system.