Near-Linear Orbit Uncertainty Propagation in the Perturbed Two-Body Problem

TL;DR

This paper introduces a method using generalized equinoctial orbital elements to significantly improve uncertainty propagation accuracy in perturbed two-body orbital models, especially considering Earth's gravity field complexities.

Contribution

The paper presents a novel application of GEqOE for near-linear uncertainty propagation in perturbed two-body problems, outperforming existing orbital element sets.

Findings

Significant reduction in non-linear effects with GEqOE

Improved uncertainty propagation accuracy in various Earth orbit scenarios

Enhanced performance in low-thrust orbit raising cases

Abstract

The paper addresses the problem of minimizing the impact of non-linearities when dealing with uncertainty propagation in the perturbed two-body problem. The recently introduced generalized equinoctial orbital element set (GEqOE) is employed as a means to reduce non-linear effects stemming from J$_2$ and higher order gravity field harmonics. The uncertainty propagation performance of the proposed set of elements in different Earth orbit scenarios, including low-thrust orbit raising, is evaluated using a Cram\'er-von Mises test on the Mahalanobis distance of the uncertainty distribution. A considerable improvement compared to all sets of elements proposed so far is obtained.