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Machine Learned Atmospheric Force Model Trained With Two Line Elements

November 29, 2023

How can machine learning enhance orbital decay predictions using atmospheric drag data?

Thousands of objects orbiting in Low Earth Orbit (LEO) are catalogued and tracked by US Space Force (USSF) in a database of Two-Line Elements (TLEs) that is available online. A time series of TLE states for a particular object will show its orbital decay over time due to atmospheric drag. The decay data across multiple objects can form a training set to create a Machine Learning (ML) model for the atmospheric drag force. This paper investigates a demonstration of this process by training a ML atmosphere model with decay data from a historical object. Regression tests of the ML model against different propagation models are performed. The process to add force modeling context to the algorithm is described.

Introduction

For objects orbiting in LEO (and in the absence of maneuvers), the atmospheric drag force is the dominant perturbation force that affects the trajectory over time. Thus, accurately modeling a time- and state-dependent atmosphere has been a high priority to enable high accuracy propagations and predictions of orbiting objects in LEO. Temporal changes in the atmosphere are largely driven by solar weather. In particular, it has been found that the atmosphere is sensitive to radio solar flux of 10.7 cm wavelength.[1] This radio frequency is observed and modeled and predictions are made from the models, which are published by various sources at various time resolutions and lengths.

 

Comparison of observed vs predicted orbital decay of a vehicle over time.

Figure 1. Comparison of observed vs predicted orbital decay of a vehicle over time.

 

However, the effect of drag upon an orbiting vehicle is observable by the changes in orbital parameters of that vehicle over time. In Fig. 1, this process is notionally plotted, an initial state is observed to decay some amount, as compared to a prediction from the initial state which calculates a different orbital decay. The difference between the observed and predicted orbital states is due to atmospheric modeling errors and forms the basis for a stochastic update to the atmospheric model to improve its predictive value.

Over each time span and across multiple missions, these errors can be organized to be the training data to an ML process that refines the atmospheric model stochastically to reduce prediction errors. In order to train such an ML process, a sufficiently sized training data set is necessary in the form of state histories of multiple LEO vehicles.

The USSF tracks and reports on the states of many orbiting objects, which are available in databases hosted online by organizations such as space-track.org and celestrack.org. The state histories of orbiting objects are formatted as TLEs. This paper investigates the feasibility of the training process and analyzes the performance of the resulting model. The performance is analyzed through a regression test comparing predicted and recorded TLE states for historical missions.

Prior work in the area of machine learning and atmospheric modeling include an analysis into a Long Short-Term Memory NN to forecast the 10.7 cm solar flux[2] and an analysis to estimate thermosphere density during quiet times and during geomagnetic storms using Gaussian processes and neural networks[3]. This work is inspired by and extends these analyses by utilizing training data of space vehicle states to model orbit decay from atmospheric drag.

Click the image below to download the white paper.

Illustrated cover for Machine Learned Atmospheric Force Model Trained With Two Line Elements white paper

References
1 Tapping, K. F. The 10.7 cm Solar Radio Flux. Space Weather Journal Vol 11, Issue 7, July 2013
2 Fry, C. A., McLaughlin, C. A. Optimizing a Long Short-Term Memory Neural Network to Forecast Solar Flux. AAS Astrodynamics Specialists Conference, August 2022
3 Wang, Y., Bai, X. Comparison of Gaussian Processes and Neural Networks for Thermospheric Density Predictions During Quiet Times and Geomagnetic Storms. AAS Astrodynamics Specialists Conference, August 2022
4 U.S. Standard Atmosphere, 1976. National Aeronautics and Space Administration. NASA- TM-X-74335
5 27-Day Outlook of 10.7 cm Radio Flux and Geomagnetic Indices. Online: https://www.swpc.noaa.gov/products/27-day- outlook-107-cm-radio-flux-and-geomagnetic- indices
6 Pesnell, W. D., Schatten, K. H. An Early Prediction of the Amplitude of Solar Cycle 25. Solar Physics Vol 293, July 2018
7 Two Line Orbital Element Set File. Online: https://ai-solutions.com/_help_Files/two-line_element_set_file.htm
8 Rasamoelina, A. D., Adjailia, F., Sinčák, P. A Review of Activation Function for Artificial Neural Network. IEEE International Symposium on Applied Machine Intelligence and Informatics, Jan 2020.
9 Raissi, M., Perdikaris, P., Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Volume 378, 2019, pp 686-707
10 Brunton, S. L. (2022, August 5), Discrepancy Modeling with Physics Informed Machine Learning
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