Orbital State Uncertainty Realism

A new class of multivariate probability density functions is proposed called the Gauss von Mises (GVM) family of distributions. The distinguishing feature of the GVM distribution is its definition on a cylindrical manifold, the underlying state space in which systems of orbital element coordinates are more accurately defined, which can provide a statistically rigorous treatment of uncertainty needed for uncertainty propagation and nonlinear filtering, orbit determination, tracking, and data association. This paper provides the initial motivation, mathematical background, and definition of the new GVM distribution along with a brief example to illustrate proof-of-concept.