An approximate model for the computation of in-orbit collision probabilities using importance sampling

Abstract

The risk of orbital collisions is at an all-time high. Standard methods which compute the probability of collision (PoC) often make restrictive assumptions which produce numerically efficient solutions, the quality of which may decrease over long time-spans. The crude Monte Carlo (CMC) simulation makes few assumptions and can produce high quality estimates; however, its computational cost can be prohibitively high. We introduce a new method based on importance sampling (IS), which aims to attain the accuracy of a CMC simulation at a fraction of the computational cost. To accomplish this, we propose a surrogate dynamical model which exploits Keplerian conjunction geometry and applies a linear correction to approximate the full-dynamics of the conjunction scenario, reducing the computational load of evaluating the dynamical model. This linear approximation is satisfactorily validated by means of high-fidelity model evaluations. The PoC results, when the method is applied on LEO and GEO scenarios, show agreement with an independent CMC benchmark simulation for the calculation of the PoC at a fraction of the computational cost.