Time-delayed Dynamic Mode Decomposition for families of periodic trajectories in Cislunar Space

TL;DR

This paper investigates data-driven Koopman operator methods for orbit prediction of periodic trajectories in cislunar space, addressing challenges like nonlinearity and sparse data, with theoretical and experimental validation.

Contribution

It introduces a Koopman-based approach for orbit prediction in cislunar space, providing theoretical justification and validation for its effectiveness in complex, nonlinear scenarios.

Findings

Koopman operator approximations effectively model cislunar trajectories.

The method accurately captures spectral content and period estimates.

The approach is validated through experiments and theoretical analysis.

Abstract

In recent years, the development of the Lunar Gateway and Artemis missions has renewed interest in lunar exploration, including both manned and unmanned missions. This interest necessitates accurate initial orbit determination (IOD) and orbit prediction (OP) in this domain, which faces significant challenges such as severe nonlinearity, sensitivity to initial conditions, large state-space volume, and sparse, faint, and unreliable measurements. This paper explores the capability of data-driven Koopman operator-based approximations for OP in these scenarios. Three stable periodic trajectories from distinct cislunar families are analyzed. The analysis includes theoretical justification for using a linear time-invariant system as the data-driven surrogate. This theoretical framework is supported by experimental validation. Furthermore, the accuracy is assessed by comparing the spectral content captured to period estimates derived from the fast Fourier transform (FFT) and Poincare-like sections.