Cislunar State and Uncertainty Propagation via the Modified Generalized Equinoctial Orbital Elements

Abstract

The complex cislunar dynamical environment poses challenges for spacecraft navigation and Space Domain Awareness (SDA) operations, where the knowledge of current and future spacecraft states is essential. Conventional Gaussian-based approaches for SDA degrade under the nonlinearities that manifest in this regime. To accurately model the underlying dynamics and characterize uncertainty, this work explores the Modified Generalized Equinoctial Orbital Elements under high-fidelity propagation for cislunar applications. The Henze-Zirkler test for multivariate normality is leveraged to evaluate uncertainty evolution across a range of orbits, demonstrating improved preservation of Gaussian behavior in cislunar space.

Figures (13)

• Figure 1: Cartesian and M-GEqOE representations of the 9:2 NRHO over $6.5 \ days$. Blue and orange curves represent the M-GEqOE and Cartesian solutions, respectively.
• Figure 2: Henze--Zirkler test applied to uncertainty propagated along the 9:2 NRHO.
• Figure 3: Pairs plot for the NRHO at the first perilune pass (${t = 3.25 \ days}$) showing projections in Cartesian (lower triangular) and M-GEqOE (upper triangular) coordinates.
• Figure 4: Eigenspace pairs plot for the NRHO at the first perilune pass (${t = 3.25 \ days}$) showing projections in Cartesian (lower triangular) and M-GEqOE (upper triangular) coordinates.
• Figure 5: Cartesian and M-GEqOE representations of the 4:1 resonant orbit over $27.30 \ days$. Blue and orange curves represent the M-GEqOE and Cartesian solutions, respectively.