Skip to main content
SpringerLink
Log in

Two-Line Element Estimation Using Machine Learning

  • Original Article
  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

Two-line elements are widely used for space operations to predict orbits with a moderate accuracy for 2-3 days. Local optimization methods can estimate a TLE as long as there exists an initial estimate, whereas global optimization methods are computationally intensive, and estimating a large number of them is prohibitive. In this paper, the feasibility of predicting the initial estimates within the radius of convergence of the actual TLEs using machine learning methods is investigated. First, a Monte-Carlo approach to estimate a TLE, when there is no initial estimate that is within the radius of convergence of the actual TLE, is introduced. The proposed Monte-Carlo method is leveraged for demonstrating the behavior of the fitting error between the realistic trajectory and the trajectory propagated by SGP4 theory during the TLE estimation processes and evaluating the unbiased performance of the proposed machine learning models. 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 9.5 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Availability of data and material

On behalf of all authors, the corresponding author states that the data and materials may be shared with interested reader.

Code Availability

On behalf of all authors, the corresponding author states that the code may be shared with interested reader.

Notes

  1. Available at http://www.space-track.com.

  2. Available at https://github.com/dmlc/xgboost.

References

  1. Hoots, R.R., Kelso, F.R.T.: Spacetrack report# 3, 1–3 (1980)

    Google Scholar 

  2. Vallado, D.A.: Fundamentals of Astrodynamics and Applications, 4th edn. Microcosm Press, Cleveland (2013)

    MATH  Google Scholar 

  3. Vallado, D., Crawford, P., Hujsak, R., Kelso, T.: Revisiting spacetrack report# 3, 6753 (2006)

    Google Scholar 

  4. Vallado, D., Crawford, P.: Sgp4 orbit determination. p 6770 (2008)

  5. Jochim, E., Gill, E., Montenbruck, O., Kirschner, M.: Gps based onboard and onground orbit operations for small satellites. Acta Astronautica 39(9-12), 917 (1996)

    Article  Google Scholar 

  6. Lee, B.: Norad tle conversion from osculating orbital element. J Astron Space Sci 19(4), 395 (2002)

    Article  Google Scholar 

  7. Montenbruck, O., Gill, E.: Real-time estimation of sgp4 orbital elements from gps navigation data. pp 26–30 (2000)

  8. Goh, S.T., Low, K.S.: Real-time estimation of satellite’s two-line elements via positioning data. pp 1–7 (2018)

  9. Bolandi, H., Ashtari Larki, M., Sedighy, S., Zeighami, M., Esmailzadeh, M.: Estimation of simplified general perturbations model 4 orbital elements from global positioning system data by invasive weed optimization algorithm. Proc Inst Mechan Eng Part G: J Aerosp Eng 229(8), 1384 (2015)

    Article  Google Scholar 

  10. Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. J Comput Syst Sci 55(1), 119 (1997)

    Article  MathSciNet  Google Scholar 

  11. Kuhn, M., Johnson, K.: Applied Predictive Modeling, vol. 26. Springer, New York (2013)

  12. Friedman, J.H.: Greedy function approximation: A gradient boosting machine. Annals Stat 1189–1232 (2001)

  13. Friedman, J.H.: Stochastic gradient boosting. Comput Stat Data Anal 38(4), 367 (2002)

    Article  MathSciNet  Google Scholar 

  14. Chen, T., Guestrin, C.: Xgboost: A scalable tree boosting system. 785–794 (2016)

  15. Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math Cont Signals Syst 2(4), 303 (1989)

    Article  MathSciNet  Google Scholar 

  16. Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw 2(5), 359 (1989)

    Article  Google Scholar 

  17. Goodfellow, I., Bengio, Y., Courville, A: Deep Learning. MIT press, Cambridge (2016)

    MATH  Google Scholar 

  18. Maisonobe, L., Pommier, V., Parraud, P.: Orekit: An open-source library for operational flight dynamics applications. 3–6 (2010)

  19. Broucke, R., Cefola, P.: On the equinoctial orbit elements. 303–310 (1972)

  20. Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization (2015)

Download references

Author information

Authors and Affiliations

  1. University of New South Wales, Canberra, Australian Capital Territory, 2600, Australia

    Rasit Abay, Sudantha Balage, Melrose Brown & Russell Boyce

Authors
  1. Rasit Abay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sudantha Balage
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Melrose Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Russell Boyce
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rasit Abay.

Ethics declarations

Declarations

Conflict of Interests

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abay, R., Balage, S., Brown, M. et al. Two-Line Element Estimation Using Machine Learning. J Astronaut Sci 68, 273–299 (2021). https://doi.org/10.1007/s40295-021-00249-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40295-021-00249-0

Keywords

Search

Navigation