Résumé : The paper investigates a new methodology to rebuild freestream conditions for the trajectory of a reentry vehicle from stagnation-point measurements. Uncertainties due to measurements and model parameters are taken into account, and a Bayesian setting supplied with metamodels is used to solve the associated stochastic inverse problem.A sensitivity analysis based on a stochastic spectral framework is first investigated to study the impact of uncertain input data on stagnation-point measurements. An original backward uncertainty propagation method is then proposed, for which only the uncertainties that have the most impact are retained.