Toroidal path filter for orbital conjunction screening

For satellite conjunction prediction containing many objects, timely processing can be a concern. Various filters are used to identify orbiting pairs that cannot come close enough over a prescribed time period to be considered hazardous. Such pairings can then be eliminated from further computation to quicken the overall processing time. One such filter is the orbit path filter (also known as the geometric pre-filter), designed to eliminate pairs of objects based on characteristics of orbital motion. The goal of this filter is to eliminate pairings where the distance (geometry) between their orbits remains above some user-defined threshold, irrespective of the actual locations of the satellites along their paths. Rather than using a single distance bound, this work presents a toroid approach, providing a measure of versatility by allowing the user to specify different in-plane and out-of-plane bounds for the path filter. The primary orbit is used to define a focus-centered elliptical ring torus with user-defined thresholds. An assessment is then made to determine if the secondary orbit can touch or penetrate this torus. The method detailed here can be used on coplanar, as well as non-coplanar, orbits.