Picard Trajectory Approximation Iteration for Efficient Orbit Propagation
This report covers the third year of the contract AFOSR Contract FA9550-11-1-0279 which has involved the effort of the principal investigator, John L. Junkins, and 5 PhD students. The project addresses a problem near the heart of space situational awareness SSA, namely efficient and accurate propagation of orbits. This is a classical problem whose importance has been dramatically elevated by the growth of orbital debris population, and by several events involving deliberate and accidental collisions of spacecraft in low earth orbit. There are numerous challenges 1 Space object catalog updates, requiring precision propagation of approximately 20,000 objects orbits 2 Conjunction analysis, probability of collision, and collision avoidance and 3 Processing of nightly observables to identify and characterize existing and new objects, requires testing of approximately 106 orbit propagation hypothesis and hours of high performance CPU time for per day. We have very significantly built on classical developments due to Picard by fusing approximation theory and a family of other advances to optimize the resulting algorithms for both serial and parallel computing environments. In contrast to classical step-by-step differential equation solvers in most common usage, the methods we are researching are path iteration methods where paths over time intervals spanning up to several orbits are approximated. In the course of this work, we have developed novel algorithms and compared them with the state of the art algorithms, and also other methods that have recently emerged in the research literature. We have also transitioned the results of this project to the GEO-Odyssey SSA project a joint effort of AFRL, NRL and NRO, involving 30 investigators in the course of this project. We have attached journal and conference papers as appendices in order to document the details.