Precise and Efficient Orbit Prediction in LEO with Machine Learning using Exogenous Variables

TL;DR

This work tackles the challenge of precise, real-time orbit prediction in Low-Earth Orbit by replacing purely physics-based propagation with a data-driven framework that leverages exogenous environmental variables to model non-conservative forces. A two-step, multi-step architecture combines a coarse time-series model (Prophet or iTransformer) with a covariate-aware FFN, trained on real CPF ephemerides of LARETS to forecast state vectors. The approach demonstrates faster inference and competitive RMSE, outperforming a J2 propagator after about one day, while remaining substantially less computationally intensive than full numerical propagation; results highlight a favorable speed-accuracy trade-off for SSA scalability. The work suggests that incorporating exogenous drivers and careful model design can yield practical, real-time orbit determination suitable for large constellations, with future enhancements including additional force models and generalization to multiple satellites.

Abstract

The increasing volume of space objects in Earth's orbit presents a significant challenge for Space Situational Awareness (SSA). And in particular, accurate orbit prediction is crucial to anticipate the position and velocity of space objects, for collision avoidance and space debris mitigation. When performing Orbit Prediction (OP), it is necessary to consider the impact of non-conservative forces, such as atmospheric drag and gravitational perturbations, that contribute to uncertainty around the future position of spacecraft and space debris alike. Conventional propagator methods like the SGP4 inadequately account for these forces, while numerical propagators are able to model the forces at a high computational cost. To address these limitations, we propose an orbit prediction algorithm utilizing machine learning. This algorithm forecasts state vectors on a spacecraft using past positions and environmental variables like atmospheric density from external sources. The orbital data used in the paper is gathered from precision ephemeris data from the International Laser Ranging Service (ILRS), for the period of almost a year. We show how the use of machine learning and time-series techniques can produce low positioning errors at a very low computational cost, thus significantly improving SSA capabilities by providing faster and reliable orbit determination for an ever increasing number of space objects.

Figures (4)

• Figure 1: Two-layer Model Architecture: Integration of two independently trained models, where one serves partially as the input source for the other.
• Figure 2: The Mean Absolute Error (MAE) calculated over a 3-day propagation window reveals that the Numerical Propagation method excels in precision compared to the ML models. Nevertheless, as the propagation period extends, the error gap between the models diminishes. After approximately $1$ day, the ML models outperform the J2 model.
• Figure 3: RMSE in the $r = (x,y,z)$ Cartesian coordinates for the Prophet + FNN model, the Numerical Propagator, the J2 Propagation and the iTransformer + FNN, respectively.
• Figure 4: Average Execution time (in seconds) for a single propagation vs RMSE. Value obtained for data in the test set, across $\approx$ 2 months. The iTransformer + FNN model is the fastest model, propagating a state every $0.018$ seconds, at the expense of being less precise than the other ML model. The y axis is in logarithmic scale.