Machine Learning in Orbit Estimation: a Survey

TL;DR

The paper surveys machine-learning applications to orbit estimation, focusing on three core tasks: Orbit Determination (OD), Orbit Prediction (OP), and Thermospheric Density modeling. It frames the problem within classical physics-based methods (e.g., EKF, SGP4, JB/DTM) and surveys ML strategies ranging from error-correction for OP, latent force models, and distribution-based uncertainty (GPs, Bayesian NNs), to grey-box reduced-order models and density-calibration approaches. It discusses limitations such as Gaussian assumptions, the need for uncertainty quantification, and the challenge of generalization to unseen RSOs, while highlighting promising directions like physics-informed neural networks and multi-model ensembles. The work underscores the potential of ML to deliver probabilistic, density-aware orbit predictions that enhance collision avoidance and improve drag-density modeling in the thermosphere, paving the way for more robust space-traffic management.

Abstract

Since the late 1950s, when the first artificial satellite was launched, the number of Resident Space Objects has steadily increased. It is estimated that around one million objects larger than one cm are currently orbiting the Earth, with only thirty thousand larger than ten cm being tracked. To avert a chain reaction of collisions, known as Kessler Syndrome, it is essential to accurately track and predict debris and satellites' orbits. Current approximate physics-based methods have errors in the order of kilometers for seven-day predictions, which is insufficient when considering space debris, typically with less than one meter. This failure is usually due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, and unknown characteristics such as the mass or geometry of the space object. Operators can enhance Orbit Prediction accuracy by deriving unmeasured objects' characteristics and improving non-conservative forces' effects by leveraging data-driven techniques, such as Machine Learning. In this survey, we provide an overview of the work in applying Machine Learning for Orbit Determination, Orbit Prediction, and atmospheric density modeling.

Figures (9)

• Figure 1: The two main stages of orbital estimation necessary for collision avoidance and debris and satellite tracking. The information obtained from OD is used as input for Orbit Prediction (OP). Figure adapted from Vallado2001 and Luo2017.
• Figure 2: General Kalman Filter Diagram. $A_k$ is the state transition matrix at time $k$, $K_k$ is the Kalman Gain at each observational moment, $H_k$ is the linear measurement mode at time step $k$, and the output is the estimated mean ($\hat{x}_k$) and covariance ($\Sigma_k$) at time step $k$. $\hat{x}_{k|k-1}$ and $\Sigma^-_k$ are internal components representing the a priori prediction before the observation $y_k$ is introduced.
• Figure 3: Uncertainty representation comparison between different filters for Orbit Determination. The blue marks are the ground truth representation using a PF. Image in Poore2016.
• Figure 4: Error Sources in Orbital Prediction, adapted from Luo2017.
• Figure 5: Illustration of the dataset structure for the ML approach to SGP4 error correction, as presented by Peng2020.