Multi-Fidelity Monte-Carlo Estimation of Satellite Drag in Very-Low-Earth Orbit

TL;DR

This paper introduces a multi-fidelity Monte Carlo method to efficiently estimate satellite drag uncertainty in very-low-Earth orbit by combining high-fidelity DSMC simulations with low-fidelity panel models.

Contribution

It develops a novel MFMC estimator that leverages panel models as control variates to reduce computational cost in drag uncertainty quantification.

Findings

MFMC reduces RMSE of drag coefficient estimates when low-fidelity models are highly correlated.

The method is validated on CubeSat and satellite configurations with thermospheric variability.

Practical factors like correlation and cost ratios influence the effectiveness of control variates.

Abstract

Very-low-Earth orbit drag uncertainty quantification in the rarefied/transitional Knudsen-number regime requires estimating not only the mean drag coefficient but also higher-order moments under atmospheric variability, which becomes prohibitively expensive when high-fidelity kinetic solvers are required. This work develops a multi-fidelity Monte Carlo (MFMC) estimator for the drag coefficient using a DSMC solver (PICLas) as the high-fidelity model and two free-molecular panel-method variants (ADBSat with Sentman and Cercignani-Lampis-Lord (CLL) gas-surface interaction models) as low-fidelity control variates. We treat E[C_D] and E[C_D^2] as the primary estimation targets and form the physically induced variance only afterwards via Var(C_D)=E[C_D^2]-(E[C_D])^2. High-fidelity reference moments are obtained from long DSMC sequences using objective convergence criteria based on sliding-window stability and 95% confidence intervals. The MFMC implementation is first numerically verified on an analytic toy model with closed-form moments, then assessed on a canonical CubeSat geometry (validation) and on SOAR, GOCE, and CHAMP configurations (verification) under MSIS-derived thermospheric variability and angle-of-attack uncertainty. When low-fidelity correlations are high for both C_D and C_D^2, MFMC reduces the relative RMSE of E[C_D] and E[C_D^2] by factors of several at matched high-fidelity-equivalent cost; improvements for Var(C_D) remain more case-dependent due to cancellation sensitivity. Overall, the study identifies practical drivers (moment correlations, cost ratios, and weight stability) that govern when panel models serve as effective control variates for DSMC-based drag uncertainty quantification.