Embodiments of the present invention characterizing the uncertainty of the orbital state of an Earth-orbiting space object hereof using a Gauss von Mises probability density function defined on the n+1 dimensional cylindrical manifold n×. Additionally, embodiments of the present invention can include transforming a Gauss von Mises distribution under a diffeomorphism and approximating the output as a Gauss von Mises distribution. Embodiments of the present invention can also include fusing a prior state represented by a Gauss von Mises distribution with an update report, wherein the update can be either another Gauss von Mises distribution of the same dimension as the prior or an observation related to the prior by a stochastic measurement model. A Gauss von Mises distribution can be calculated from a plurality of reports, wherein the reports are either Gauss von Mises distributions or observations related to the state space by a stochastic measurement model.