Orbital error propagation analysis using directional statistics for space objects

As increasing numbers of optical line-of-sight observations become available for space objects, the space situational awareness community is presented with the computationally challenging problem of representing the uncertainty efficiently and accurately. The motion of a space object in orbit about the earth is described by Newtonian mechanics. More specifically, if measurements for the position and velocity at an initial time are available up to Gaussian noise, then point clouds are typically used to describe the propagated uncertainty at later times. In this paper we show that it is possible to describe succinctly the angular part of the position vector at later times using a version of the Fisher-Bingham-Kent distribution from directional statistics.