Extend GEqOE to include continuous process noise

Develop an extension of the Generalized Equinoctial Orbital Elements (GEqOE) framework that includes continuous process noise, enabling a stochastic GEqOE formulation for orbital uncertainty propagation.

Background

The Generalized Equinoctial Orbital Elements (GEqOE) have been shown to render orbital dynamics nearly linear for deterministic propagation, improving the fidelity of Gaussian-based uncertainty propagation relative to Cartesian coordinates over long arcs.

In the paper’s outlook, the authors note that while GEqOE is effective for deterministic cases, it currently lacks a formulation that incorporates continuous process noise. They explicitly identify this as an open problem and suggest that the Taylor Map Diffusion framework developed in the paper could provide a pathway to address it.