Machine Learning Argument of Latitude Error Model for LEO Satellite Orbit and Covariance Correction

TL;DR

This work tackles the problem of accurate long-horizon orbit propagation for LEO satellites under drag mismodeling, a key bottleneck for alternative PNT systems to GNSS. It proposes a machine learning framework that learns AOL error distributions from VCM-ephemerides and a SP propagator, producing Gaussian AOL corrections that map into the Cartesian state while inflating covariance along the corrected dimensions. The study compares a time-conditioned neural network and a heteroscedastic Gaussian process, finding that both reduce propagated errors by about 50% and improve covariance consistency, with TCNN delivering better short-term corrections and HGP offering better time generalization. Practically, this approach extends the usefulness of VCM covariances over longer horizons and enables more robust selection of satellites for navigation in environments where drag mismodeling is significant.

Abstract

Low Earth orbit (LEO) satellites are leveraged to support new position, navigation, and timing (PNT) service alternatives to GNSS. These alternatives require accurate propagation of satellite position and velocity with a realistic quantification of uncertainty. It is commonly assumed that the propagated uncertainty distribution is Gaussian; however, the validity of this assumption can be quickly compromised by the mismodeling of atmospheric drag. We develop a machine learning approach that corrects error growth in the argument of latitude for a diverse set of LEO satellites. The improved orbit propagation accuracy extends the applicability of the Gaussian assumption and modeling of the errors with a corrected mean and covariance. We compare the performance of a time-conditioned neural network and a Gaussian Process on datasets computed with an open source orbit propagator and publicly available Vector Covariance Message (VCM) ephemerides. The learned models predict the argument of latitude error as a Gaussian distribution given parameters from a single VCM epoch and reverse propagation errors. We show that this one-dimensional model captures the effect of mismodeled drag, which can be mapped to the Cartesian state space. The correction method only updates information along the dimensions of dominant error growth, while maintaining the physics-based propagation of VCM covariance in the remaining dimensions. We therefore extend the utility of VCM ephemerides to longer time horizons without modifying the functionality of the existing propagator.

Figures (9)

• Figure 1: Machine learning model predicts errors and variance in the argument of latitude to correct both the propagated orbit and covariance for a variety of LEO orbit and satellite types.
• Figure 2: Orbit propagation correction pipeline using VCMs, open source SP propagator, and machine learning model.
• Figure 3: Accelerations due to individual force models in Orekit orbit propagator over various altitudes for an example satellite in an initially circular orbit with a ballistic coefficient of 0.13 $m^2/kg$.
• Figure 4: Example of error growth for propagation of a single VCM (NORAD ID 47). True AOL error maps to predominantly along-track position and radial velocity dimensions. Errors in the remaining dimensions are caused by errors in other orbital elements and therefore are not captured by argument of latitude.
• Figure 5: Over 95% of the norm position error is captured by the argument of latitude after 5 day propagation (NORAD ID 47).