Kustaanheimo–Stiefel - Cartesian orbital covariance transformation

Orbital uncertainty propagation tasks have become the computational bottleneck in many astronomical and astrodynamical applications: Monte Carlo-based strategies lie at the state of the art, given the high non-linearity of the dynamics. For this reason, several methods to mitigate the computational intensity of such problems have been studied. On one side, alternative statistical approaches are being explored while relying on a fully non-linear description using Cartesian variables. At the same time, more computationally efficient formulations of the equations of motion have been proposed. This work focuses on a relatively unexplored preliminary step of the general uncertainty propagation problem, analyzing the transformation of the orbital uncertainty between different dynamical formulations, with the ultimate goal of enabling the use of more efficient models of the strongly non-linear gravitational interactions. In particular, the case of the covariance conversion between Cartesian and Kuustanheimo-Stiefel (KS) realms is studied, as it also poses the challenges of transformation between phase spaces of different dimensions and of the introduction of a fictitious time as independent dynamics' variable.