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

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.

probability of collision; space situational awareness; conjunction geometry; dimensionality reduction; importance sampling; monte carlo

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