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The Space Situational Awareness (SSA) program places great significance on obtaining high-resolution images of satellite in space orbit. By utilizing space-borne inverse synthetic aperture radar (SBISAR) can achieve high-resolution imaging of Observed satellite (OS) on-orbit especially in geosynchronous orbit (GEO). However, the complex and nonuniform relative motion of the OS on-orbit and SBISAR produces 2-D spatial variant phase errors, which has a high-order form during long coherent processing intervals (CPI). Up to now, the imaging problem of SBISAR has not been effectively tackled. In this work, a novel method to compensate for the 2-D spatial variant phase errors for SBISAR imaging based on minimum entropy and quasi-Newton&#x0027;s method is proposed. First, the geometric model that considers the relative motion state of SBISAR and the OS on-orbit is established and the optimal observation time period is determined. Second, we propose the echo signal model for the satellite on-orbit and deduce the specific form of the high-order spatial variant phase errors. Third, based on image entropy (IE), quasi-Newton&#x0027;s method is adopted to obtain the optimal solution for the phase error coefficients. Finally, a new initial estimation method that aims to overcome the local convergence of quasi-Newton&#x0027;s method is proposed. By utilizing the optimal parameters, the well-focused SBISAR image can be achieved. Taking GEO satellite imaging as an example, experiments based on scattering point simulation data verify the effectiveness of the proposed method.

An Effective Space-Borne ISAR High-Resolution Imaging Approach for Satellite On-Orbit Based on Minimum Entropy Optimization