  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.
