Nonlinear Uncertainty Propagation in Astrodynamics Using Differential Algebra and Graphics Processing Units

In this paper, two numerical methods for nonlinear uncertainty propagation in astrodynamics are presented and thoroughly compared. Both methods are based on the Monte Carlo idea of evaluating multiple samples of an initial statistical distribution around the nominal state. However, whereas the graphics processing unit implementation aims at increasing the performances of the classical Monte Carlo approach exploiting the massively parallel architecture of modern general-purpose computing on graphics processing units, the method based on differential algebra is aimed at the improvement and generalization of standard linear methods for uncertainty propagation. The two proposed numerical methods are applied to test cases considering both simple two-body dynamics and a full n-body dynamics with accurate ephemeris. The results of the propagation are thoroughly compared with particular emphasis on both accuracy and computational performances.