Propagation of grid-scale density model uncertainty to orbital uncertainties

Abstract

Accurate knowledge of the orbital state-vector uncertainty is required for the computation of reliable collision probabilities, the association of tracks, as well as the optimal planning of sensor resources. In low Earth Orbits (LEO) neutral atmospheric density uncertainty is the main contributor to orbital state vector uncertainty. Grid-scale model uncertainty on the other hand is, in most cases, the dominating component of atmospheric density uncertainty.Prior research in the field of density uncertainty has been broad. Nowadays multiple authors seem to agree that a first-order stochastic Gauss-Markov process, also known as Ornstein-Uhlenbeck process (OUP), is an appropriate stochastic representation for density model uncertainties. While many have studied orbital variations due to stochastic grid-scale density uncertainty, it is believed that the work at hand provides for the first time explicit analytic equations for the estimation of orbital uncertainties due to an underlying Ornstein-Uhlenbeck process that has been optimized for the representation of atmospheric density. It is shown that the long-term in-track position error due to this modified OUP grows with ~t3.The presented derivations and their validation build upon prior work by Emmert et al. and Sagnières and Sharf. Numerical Monte-Carlo simulations are used to validate the findings with two different semi-empirical density models. We also demonstrate that the resulting orbital uncertainty due to the modified OUP in atmospheric density can be estimated using a classical OUP in the relative density error.