# Two-Line Element Estimation Using Machine Learning

## TL;DR

This paper explores machine learning techniques, including Monte-Carlo methods and neural networks, to estimate Two-Line Elements (TLEs) for space objects, achieving high accuracy with reduced computational effort.

## Contribution

It introduces a Monte-Carlo approach for TLE estimation without initial guesses and trains ML models to map orbital evolution to TLEs using large datasets.

## Key findings

- Monte-Carlo method achieves residual errors below 1 km.
- ML models successfully estimate TLEs for certain cases.
- The approach reduces computational costs compared to traditional methods.

## Abstract

Two-line elements are widely used for space operations to predict the orbit with a moderate accuracy for 2-3 days. Local optimization methods, such as the nonlinear least squares method with differential corrections, can estimate a TLE as long as there exists an initial estimate that provides the desired precision. Global optimization methods to estimate TLEs are computationally intensive, and estimating a large number of them is prohibitive. In this paper, the feasibility of estimating TLEs using machine learning methods is investigated. First, a Monte-Carlo approach to estimate a TLE, when there are no initial estimates that provide the desired precision, is introduced. The proposed Monte-Carlo method is shown to estimate TLEs with residual mean squared errors below 1 km for space objects with varying area-to-mass ratios and orbital characteristics. Second, gradient boosting decision trees and fully-connected neural networks are trained to map the orbital evolution of space objects to the associated TLEs using 8 million publicly available TLEs from the US space catalog. The desired precision in the mapping to estimate a TLE is achieved for one of the three test cases, which is a low area-to-mass ratio space object.