Skip to main content
SpringerLink
Log in

Identifying Cislunar Orbital Families via Machine Learning on Light Curves

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

Abstract

Current methods of performing Initial Orbit Determination (IOD) in near-earth orbital regions cannot be directly extended to cislunar space due to changes in gravitational models that must be utilized. For the case of cislunar orbits, the Moon’s gravitational influence necessitates that orbital motions be described by three-body dynamics. Three-body dynamics produce orbits that are generally not elliptical, fixed to an orbital plane, or geometrically simple. This change in assumptions that can be made complicates the task of performing IOD and has led to the investigation of alternative methods and features to classify cislunar orbit parameters. In this paper, we explore the potential of utilizing Machine Learning (ML) algorithms to constrain potential IOD search spaces to specific cislunar families. We accomplish this by training the ML classifier to predict cislunar family from a light curve. To generate training data for this ML effort, we introduce a novel simulation pipeline that produces radiometrically validated light curves using the Digital Imaging and Remote Sensing Image Generation (DIRSIG™) engine. This pipeline ingests various parameters, including: initial Circular Restricted Three-Body Problem (CR3BP) state vectors, satellite material properties, telescope optical properties, and satellite 3D models. The pipeline produces light curves capturing the influence of these factors on the observed visual magnitude signature as a function of elapsed time and phase angle. This pipeline was utilized to produce approximately 3500 light curves of various cislunar orbital families as captured from the perspective of two observing locations: the spaced-based Earth-Moon L1 point, and a Lunar surface based point. These light curves were used as training datasets for neural network models to perform classification of cislunar family via input time-series vectors consisting of two features: visual magnitude and phase angle. Our machine learning technique first uses a warping technique to construct constant sized observational input of the light curves into a multi-layer perceptron, the architecture of which was chosen by a search over a large landscape of possibilities optimizing for validation prediction accuracy. The selected model was then trained on various scenarios of input data, again doing a search over several available hyper-parameters. It was found that the trained models were able to achieve test data-set accuracy of 93.4% for light curves captured from the face of the moon, and 87.5% when combined with light curves captured from the space-based L1 point.

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
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Northern Sky Research: Moon Market Analysis, 2nd edn. (2022)

  2. Wishnek, S., Holzinger, Marcus, J., Handley, P.: Robust cislunar initial orbit determination. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2021)

  3. Vallado, D.A.: Fundamentals of Astrodynamics and Applications, vol. 12. Springer (2001)

    Google Scholar 

  4. Martin, G., Wetterer, C.J., Lau, J., Case, J., Toner, N., Chow, C.C., Dao, P.: Cislunar periodic orbit family classification from astrometric and photometric observations using machine learning. In: 2020 Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2020)

  5. Zuehlke, D., Yow, T., Posada, D., Nicolich, J., Hays, C.W., Malik, A., Henderson, T.: Initial orbit determination for the CR3BP using particle swarm optimization. arXiv preprint arXiv:2207.13175, (2022)

  6. Holzinger, M.J., Chow, C.C., Garretson, P.: A primer on cislunar space. Technical report, Air Force Research Laboratory (2021)

  7. Vendl, J.K., Holzinger, M.J.: Cislunar periodic orbit analysis for persistent space object detection capability. J Spacecr Rockets 58(4), 1174–1185 (2021)

    Article  Google Scholar 

  8. Bolden, M., Craychee, T., Griggs, E.: An evaluation of observing constellation orbit stability, low signal-to-noise, and the too-short-arc challenges in the cislunar domain. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2020)

  9. Channing Chow, C., Wetterer, C.J., Baldwin, J., Dilley, M., Hill, K., Billings, P., Frith, J.: Cislunar orbit determination behavior: processing observations of periodic orbits with gaussian mixture model estimation filters. J. Astron. Sci. 69(5), 1477–1492 (2022)

    Article  Google Scholar 

  10. Goodenough, A.A., Brown, S.D.: DIRSIG 5: core design and implementation. In: Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVIII, volume 8390, pages 124–132. SPIE (2012)

  11. Koblick, D.C., Choi, J.S.: Cislunar orbit determination benefits of moon-based sensors. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2022)

  12. Zimmer, P., McGraw, J., Ackermann, M.: Cislunar SSA/SDA from the lunar surface: COTS imagers on commercial landers. In: Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conference (2021)

  13. Goodenough, Adam A., Brown, Scott D.: DIRSIG5: next-generation remote sensing data and image simulation framework. IEEE J Sel Top Appl Earth Observ Remote Sens 10(11), 4818–4833 (2017)

    Article  Google Scholar 

  14. Bennett, D.A., Dank, J.A., Tyler, D.W., Gartley, M., Allen, D.: SSA modeling and simulation with DIRSIG. In: Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conference, (2014)

  15. Szebehely, V., Grebenikov, E.: Theory of orbits-the restricted problem of three bodies. Soviet Astron. 13, 364 (1969)

    Google Scholar 

  16. Frueh, C., Howell, K., DeMars, K.J., Bhadauria, S.: Cislunar space situational awareness. In: 31st AIAA/AAS Space Flight Mechanics Meeting, AAS 21-290 (2021)

  17. Fowler, E.E., Paley, D.A.: Observability metrics for space-based cislunar domain awareness. J. Astron. Sci. 70(2), 10 (2023)

    Article  Google Scholar 

  18. Bolliger, M.J.: Cislunar mission design: transfers linking near rectilinear halo orbits and the butterfly family. PhD thesis, Purdue University Graduate School (2019)

  19. Parker, J.S., Anderson, R.L.: Low-energy lunar trajectory design, vol. 12. Wiley (2014)

    Book  Google Scholar 

  20. Geisel, C.D.: Spacecraft orbit design in the circular restricted three-body problem using higher-dimensional poincaré maps. PhD thesis, Purdue University (2013)

  21. Rhodes, B.: Skyfield: high precision research-grade positions for planets and earth satellites generator. Astrophysics Source Code Library, ascl:1907.024 (2019)

  22. Rhodes, B.: How to get earth-centered, earth-fixed coordinates from Skyfield? Space Stack Exchange. https://space.stackexchange.com/a/13671. Accessed 1 Sept 2023

  23. Park, R.S., Folkner, W.M., Williams, J.G., Boggs, D.H.: The JPL planetary and lunar ephemerides DE440 and DE441. Astron. J. 161(3), 105 (2021)

    Article  Google Scholar 

  24. Kardol, S.: An interactive, web-based, near-earth orbit visualization tool. Master thesis (2018)

  25. Velez-Reyes, M., Erives, H., Najera, A., Chun, F., Plis, E., Badura, G., Reyes, J., Gartley, M., Hope, D.: Understanding non-resolved space object signatures for space domain awareness. In: Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conference (2022)

  26. Frueh, C., Little, B., McGraw, J.: Optical sensor model and its effects on the design of sensor networks and tracking. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2019)

  27. Plis, E., Bengtson, M., Engelhart, D.P., Badura, G., Scott, T., Cowardin, H., Reyes, J., Hoffmann, R., Sokolovskiy, A., Ferguson, D.C., et al. Characterization of novel spacecraft materials under high energy electron and atomic oxygen exposure. In AIAA SciTech 2022 Forum, AIAA 2022-0797 (2022)

  28. Plis, E.A., Bengtson, M.T., Engelhart, D.P., Badura, G.P., Cowardin, H.M., Reyes, J.A., Hoffmann, R.C., Sokolovskiy, A., Ferguson, D.C., Shah, J.R., et al.: Ground testing of the 16th materials international space station experiment materials. J. Spacecr. Rockets 60(2), 1–6 (2023)

    Article  Google Scholar 

  29. Reyes, J.A., Plis, E.A., Hoffmann, R.C., Badura, G.P., Shah, J.R., Collman, S.E.J., Bengtson, M.T., Engelhart, D.P.: Spectral characterization of modern spacecraft materials. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2022)

  30. Badura, G., Plis, E., Valenta, C.: Extending laboratory brdf measurements towards radiometric modeling of resident space object spectral signature mixing. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2021)

  31. Ward, G.J.: Measuring and modeling anisotropic reflection. In: Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, pp. 265–272 (1992)

  32. Coder, R.D., Holzinger, M.J.: Multi-objective design of optical systems for space situational awareness. Acta Astron. 128, 669–684 (2016)

    Article  Google Scholar 

  33. Vaquero, M., Senent, J.: Poincaré: A multi-body, multi-system trajectory design tool. In: 7th International Conference on Astrodynamics Tools and Techniques (2018)

  34. Van der Maaten, L., Hinton, G.: Visualizing data using t-SNE. J. Mach. Learn. Res. 9(11), 2579–2605 (2008)

    Google Scholar 

  35. Furfaro, R., Linares, R., Reddy, V.: Shape identification of space objects via light curve inversion using deep learning models. In: Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conference (2019)

  36. Smith, L.I.: A tutorial on principal components analysis (2002)

  37. Bottou, L.: Large-scale machine learning with stochastic gradient descent. In: Proceedings of COMPSTAT’2010: 19th International Conference on Computational StatisticsParis France, August 22-27, 2010 Keynote, Invited and Contributed Papers, pp. 177–186. Springer (2010)

  38. Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. In: Proceedings of the 3rd International Conference on Learning Representations (ICLR) (2014)

  39. Zhang, Z., Sabuncu, M.: Generalized cross entropy loss for training deep neural networks with noisy labels. In: Advances in Neural Information Processing Systems, p. 31 (2018)

  40. Dao, P., Haynes, K., Frey, V., Hufford, C., Schindler, K., Payne, T., Hollon, J.: Simulated photometry of objects in cislunar orbits. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2020)

  41. Bolden, M., Hussein, I., Borowski, H., See, R., Griggs, E.: Probabilistic initial orbit determination and object tracking in cislunar space using optical sensors. In: Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conference, pp. 27–30 (2022)

Download references

Acknowledgements

We would like to thank GTRI’s Independent Research and Development (IRAD) funds for supporting this work. On behalf of all authors, the corresponding author states that there is no conflict of interest.

Author information

Authors and Affiliations

  1. Georgia Tech Research Institute, Atlanta, USA

    Gregory P. Badura & Nathan Un

  2. The University of Texas at El Paso, El Paso, USA

    Dan DeBlasio, Aryzbe Najera, Ana C. Chavez-Lopez & Miguel Velez-Reyes

  3. Georgia Institute of Technology, Atlanta, USA

    Yuri Shimane & Koki Ho

Authors
  1. Gregory P. Badura
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dan DeBlasio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aryzbe Najera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ana C. Chavez-Lopez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Miguel Velez-Reyes
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Nathan Un
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yuri Shimane
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Koki Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gregory P. Badura.

Additional information

Publisher's Note

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

Appendix

Appendix

Table 6 gives an overview of the initial state vectors that were used to generate light curves for this study.

Table 6 Initial dimensionless state vectors of the cislunar satellite targets that were used to generate light curves in this study for both a lunar-based telescope and a space-based telescope at the Earth-Moon L1 point
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Badura, G.P., DeBlasio, D., Najera, A. et al. Identifying Cislunar Orbital Families via Machine Learning on Light Curves. J Astronaut Sci 71, 27 (2024). https://doi.org/10.1007/s40295-024-00447-6

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40295-024-00447-6

Keywords

Search

Navigation