Multifidelity Monte Carlo for the estimation of spacecraft re-entry windows

• We present an efficient Monte Carlo estimation method (the multifidelity Monte Carlo) applied to the computation of expected re-entry time, based on an arbitrary number of dynamical models, out of which some may be computationally expensive and others, relatively efficient. • We employ the MFMC to, in addition, compute re-entry windows which safely contain the Monte Carlo distribution of an independent Monte Carlo simulation, as well as the real decay time reference. • The computed window is constructed by computing independent estimators for the upper and lower bounds of the window, and no assumption on the symmetry of such a window is made, in contrast with the literature. • In addition to the well-studied re-entry case of GOCE in 2013, the test cases used in this paper include the recent Kosmos-482 descent module re-entry of May 2025, which sparked international concern and lead to a global effort to predict the time and location of the re-entry, which was shrouded in uncertainty days prior. Our results show promising ways of obtaining accurate results at a fraction of the computational cost of crude Monte Carlo simulations. In the absence of a robust and standardized method to safely capture and deorbit spacecraft at the end of their operational lifespan, many space objects are left to undergo uncontrolled and often unpredictable atmospheric re-entry. Current re-entry prediction techniques generally rely on orbital propagation models that assume Gaussian uncertainties. While convenient, this assumption often fails to capture the strongly non-Gaussian evolution of the probability density function, particularly when nonlinear orbital dynamics couple with the stochastic and highly uncertain nature of atmospheric drag. As a result, obtaining reliable estimates for re-entry times becomes challenging. Crude Monte Carlo simulations can, in principle, yield accurate characterizations of the state distribution at the point of atmospheric decay—provided that a sufficiently large number of samples is used. However, the computational cost of performing such simulations with high-fidelity models is often prohibitive. To address this issue, we propose a multifidelity Monte Carlo framework that efficiently estimates decay time intervals by strategically allocating computational effort between low-fidelity and high-fidelity dynamical models. The approach is demonstrated on a re-entry scenario involving two decaying spacecraft missions, Kosmos-482 (2025) and GOCE (2013), where bounds on the expected decay window are computed. These results are validated against a ground-truth decay time (represented by the timestamp of the last known observation) and compared with estimates obtained from a high-fidelity crude Monte Carlo simulation.