A tri-static ground-based laser ranging method for precise satellite attitude determination

Abstract: The ability to accurately determine the rotation rate and spin axis of active satellites during deployment, during phases of uncertain operations (e.g. loss of control, potential fuel leaks) and particularly for defunct satellites to assess suitability of removal of space objects by active debris removal is increasingly important. Conventional techniques, such as optical photometry, face challenges in providing precise attitude information. In this work, we propose a tri-static ground-based satellite laser ranging (SLR) approach combined with three onboard laser retroreflectors for precise satellite attitude determination. Via this approach our method achieves true 3D triangulation of the reflectors' positions in space, enabling a highly accurate estimation of the satellite's attitude. This multi-station configuration overcomes limitations of existing single-station SLR techniques that rely on indirect inference, e.g. Fourier analysis of range residuals, or lead to multiple possible attitude solutions. We demonstrate through simulations that our approach can estimate the spin rate and axis of a satellite with high precision, on the order of 0.1 deg/sec and 1 deg, respectively. Notably, this can be done with data from only a single pass and does not require observation of a whole satellite rotation period. We show how the layout of retroreflectors are paramount to the effectiveness of the method. We provide placement strategies to maximize attitude determination performance to allow operators to incorporate retroreflectors effectively into their own satellites. These contributions lay the groundwork for a complete ground-based solution for attitude determination, significantly improving current methods and directly supporting ADR efforts.