Synthetic orbit uncertainty generation through regression analysis of historical Conjunction Data Messages

Abstract

In the last decades, the Earth-orbiting population of both active and non-active objects has grown significantly, leading to a substantial increase in number of possible in-orbit collisions. It is therefore crucial to monitor the orbit of space resident objects to assess in advance the threat of risky conjunctions. Within this framework, the 18th Space Defense Squadron (SDS) is consistently updating the orbit of thousands of tracked objects by processing observations of the U.S. Space Surveillance Network (SSN). The determined orbital data is continuously maintained in the Special Perturbation (SP) catalogue and used by the 19th SDS to issue close approach warnings to satellite operators around the globe in the form of Conjunction Data Messages (CDM). The Flight Dynamics (FD) group of the German Space Operation Centre (GSOC) receives on regular basis a subset of the SP catalogue data along with CDMs associated to the fleet of its controlled satellites. The SP ephemerides are in fact provided without any covariance information preventing any computation of the Probability of Collision (Pc). In GSOC FD we are implementing a service to link a series of synthetic orbital error covariance matrices to a given SP ephemeris by statistically analyzing historical CDMs of past events. More than 30 GB of past conjunction data are processed to extract state vector, covariance matrix and object size parameter of already encountered secondary objects. The orbital errors of these last are subsequently categorized and divided into orbital classes to decouple the high correlation the covariance has with respect to solar flux, object dimension, altitude of perigee, eccentricity and orbit inclination. The classification aims at collecting similar CDMs regarding the aforementioned dependencies, and approximates the predicted 1-sigma position errors in the orbital frame by optimal curve-fitting techniques. By evaluation of the curve fitting coefficients of a requested orbit class a covariance matrix can be generated for any prediction time in upcoming CDM refinements and other analyses. The work discusses the limiting cases of the classification approach, bringing possible solutions to the scenario of empty classes. An in-depth characterization of the parameters that affect the orbital errors is in fact performed to individualize the neighboring class that provides the closest and most meaningful covariance timeline. Successively, the effect of using synthetic covariance in a conjunction risk assessment is also explored, adapting the problem on real operations. Lastly, the entire data processing pipeline and how the described service fits into the GSOC Flight Dynamics System (FDS) framework is described.