Gauss von Mises Distribution for Improved Uncertainty Realism in Space Situational Awareness

Joshua T. Horwood, Aubrey B. Poore
2014 SIAM/ASA Journal on Uncertainty Quantification  
In order to provide a more statistically rigorous treatment of uncertainty in the space surveillance tracking environment, 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. When specialized to GVM distributions, the
more » ... ibutions, the prediction step of the general Bayesian nonlinear filter is shown to be tractable and viable, thereby providing a novel means to propagate space object orbital uncertainty under nonlinear perturbed two-body dynamics. Results demonstrate that uncertainty propagation with the new GVM distribution can be achieved at the same cost as the traditional unscented Kalman filter and can maintain "uncertainty realism" for up to eight times as long.
doi:10.1137/130917296 fatcat:ytj5nsrnmnckbjrg3aotyc4d4a