Resolution Analysis of Passive Synthetic Aperture Imaging of Fast Moving Objects

In this paper we introduce and analyze a passive synthetic aperture radar system motivated by space surveillance radar networks for detecting, tracking, imaging, and identifying small debris (aka target) in low-earth orbit. We propose a system with a powerful transmitter on the ground and one or several flying receiver platforms. Each platform can separate the direct signals from the source, coming from below, and the reflected signals, coming from above. In the case of a single receiver platform, the image is formed by cross correlating the Doppler-compensated direct and reflected signals. We show that its resolution is described by the ideal Rayleigh resolution formulas. That is, range resolution is proportional to the transmitter pulse width, and the cross range resolutions are determined by the synthetic angular cones determined by the target and receiver trajectories. However, the one-receiver imaging modality is not capable of determining both the target location and velocity. In the case of multiple receiver platforms, the image is computed by cross correlating the Doppler-compensated reflected signals. In this case, the image focusing relies on differences of travel times between the moving target and the receivers, and we show that two well separated pairs of receiver platforms are sufficient for determining the target location and velocity. The resolution formulas for this imaging modality are new and different from the Rayleigh resolution limits. They are derived analytically from first principles, and are validated with detailed numerical simulations.