Local Orbital Elements and Directional Statistics for Cislunar Space Situational Awareness

The past year and a half has been marked with an increasing cadence of exciting space missions by both nation states and private actors toward the Moon and greater cislunar domain.  With the manifest for cislunar missions only increasing in the years ahead, questions that haven't yet needed to be addressed outside of Earth-bound space missions are suddenly relevant and pressing.  In this talk, we address one of these questions; how agencies such as the United States Space Force might conduct efficient space situational awareness (SSA).  Unlike the case of SSA in low Earth orbits, the cislunar domain has strikingly rich dynamics and limited passive and weak observations, making essential steps of SSA, which includes uncertainty propagation, much more challenging.  We present in this talk a formulation that leverages dynamical systems theory to generate local orbital elements upon which probability distributions can be more naturally defined and demonstrate how doing so helps to improve the accuracy, efficiency, and realism of uncertainty propagation in the cislunar domain.