Probability of collision between space objects including model uncertainty.

Abstract An adaptive Collision Risk Assessment Tool (CRATER) is introduced in order to analyze conjunctions featuring non Gaussian distributions, long encounter times, and considerable model uncertainty. The algorithm makes use of the Fokker Planck equation to quantify the error in various assumptions, refine approximations of the propagated probability density functions (PDFs), and assess the need for external validation in some scenarios. A Local Gaussian approximation of the non-Gaussian propagated PDFs is introduced and shown to be comparable to Gaussian Mixture methods (GMM) in terms of accuracy, while exhibiting superior performance in terms of speed. The algorithm is made adaptive through the use of a non linearity index, which is used to determine the number of mixture components needed in a GMM or the spacing of local Gaussians when approximating the propagated PDFs. Coppola's method for calculating the probability of collision (PC) between space objects is modified to considering parametric model uncertainty. The PC integral is then incorporated into CRATER. CRATER is then used to compute the PC for 8 different test cases and is compared to Monte Carlo results. Highlights • New algorithm for probability of collision analysis is tested on eight test cases. • Model uncertainty shown to affect collision probability by orders of magnitude. • Alternative to gaussian mixture method shown to be faster with similar accuracy. • Error in assumptions are quantified with respect to Liouville equation. [ABSTRACT FROM AUTHOR]