Generalized Bernoulli Gauss von Mises Distribution for Uncertainty Realism on Saddle-Center Spaces

Most aspects of space situational awareness (SSA) rely on accurate and efficient uncertainty realism, propagation, and nonlinear filtering. A new frontier for SSA is the application to the cislunar realm, which lacks a global orbital element coordinate set. The dynamics of a representative model, the circular restricted three-body problem (CR3BP), for the cislunar domain provides the opportunity to define local orbital elements using dynamical systems techniques such as normal form theory. Motivated the structure of the CR3BP SSA problem, we construct a generalized Bernoulli Gauss von Mises distribution, that is defined on local orbit element coordinates generated from normal form theory at a saddle-center-center equilibrium point, and show its ability to capture what may be a common deformation mode of the CR3BP.