Relative Orbit Design and Optimization for Distributed SAR Formations

The effectiveness of swath and Doppler spectrum reconstruction algorithms in cross-track and along-track multistatic synthetic aperture radar (SAR) formations heavily relies on the precise relative positioning of each spacecraft. Ideally, a static array configuration is desired, where the satellites are evenly distributed in an Earth-fixed frame. However, maintaining this ideal configuration is not feasible without constant active flight control to counter the satellites’ relative dynamics. Alternatively, one can design natural trajectories that result in the desired formation geometry within an acceptable margin for a significant fraction of the orbital period. In this paper, we present a relative motion description in an Earth-fixed geometry for distributed SAR concepts. We derive a general expression for the transformation matrix from the Hill-Clohessy-Wiltshire (HCW) frame to the SAR-appropriate zero-Doppler (ZD) frame, and propose a general optimization method to fit the best natural non-drifting formation solution for any desired formation configuration. By applying the developed technique to optimize along-track and cross-track relative positioning requirements, we obtain conforming baselines over extended orbit stretches. We present SAR imaging examples for along-track distributed formations and formations with small cross-track baselines, using distributed platforms spanning a 72° latitude range. The demonstrated configurations achieve orbit duty cycles exceeding 20%, with baseline errors kept below 5% relative to the ideal array element positions. These results indicate the feasibility of these concepts using natural orbit solutions.