A differential algebra-based importance sampling method for impact probability computation on Earth resonant returns of near-Earth objects

A differential algebra-based importance sampling method for uncertainty propagation and impact probability computation on the first resonant returns of near-Earth objects is presented in this paper. Starting from the results of an orbit determination process, we use a differential algebra-based automatic domain pruning to estimate resonances and automatically propagate in time the regions of the initial uncertainty set that include the resonant return of interest. The result is a list of polynomial state vectors, each mapping specific regions of the uncertainty set from the observation epoch to the resonant return. Then, we employ a Monte Carlo importance sampling technique on the generated subsets for impact probability computation. We assess the performance of the proposed approach on the case of asteroid (99942) Apophis. A sensitivity analysis on the main parameters of the technique is carried out, providing guidelines for their selection. We finally compare the results of the proposed method to standard and advanced orbital sampling techniques.