Relative Orbit Design and Optimization for Distributed SAR Formations

Abstract

The effectiveness of swath and Doppler spectrum reconstruction algorithms in 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 may not feasible without constant active flight control to counter the relative dynamics of the satellites, resulting in high fuel consumption for formation maintenance. 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, which is expected to result in more efficient solutions. In this article, 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 nondrifting 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.