Estimation of a launch vehicle stage fallout zone with parametric and non-parametric importance sampling algorithms in presence of uncertain input distributions

The estimation of launch vehicle fall back safety zone is a crucial problem in space application since the consequence of a mistake may be dramatic for the population. It consists in estimating the probability that the distance between the launcher stage fall-back position calculated, with a trajectory simulation code, and the predicted one is lower than a given threshold. This probability of having a distance that exceeds the critical limit is of course low and may hardly be estimated with crude Monte Carlo methods. One proposes in this paper adaptive importance sampling algorithms when some parameters of input probability density suffer from uncertainty. This situation is a difficult issue for computational reasons since a complete importance sampling procedure is necessary to estimate the rare event probability associated to each combination of input density parameters. It is no more the case with the proposed parametric and non-parametric approaches based on the definition of a more adapted initial sampling density.