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

arXiv: https://arxiv.org/abs/2602.16764 · HTML: https://mlsanity.com/paper/2602.16764/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Multivariate Uncertainty in Deep Learning](https://mlsanity.com/paper/1910.14215/) (2019)
- [Machine Learning in Orbit Estimation: a Survey](https://mlsanity.com/paper/2207.08993/) (2022)
- [Learning to Forecast Aleatoric and Epistemic Uncertainties over Long Horizon Trajectories](https://mlsanity.com/paper/2302.08669/) (2023)

## Abstract (arXiv)

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.