Remediating Non-Positive Definite State Covariances for Collision Probability Estimation

The NASA Conjunction Assessment Risk Analysis team estimates the probability of collision (Pc) for a set of Earth-orbiting satellites. The Pc estimation software processes satellite position+velocity states and their associated covariance matri-ces. On occasion, the software encounters non-positive definite (NPD) state co-variances, which can adversely affect or prevent the Pc estimation process. Inter-polation inaccuracies appear to account for the majority of such covariances, alt-hough other mechanisms contribute also. This paper investigates the origin of NPD state covariance matrices, three different methods for remediating these co-variances when and if necessary, and the associated effects on the Pc estimation process.