Abstract
In this paper, the recently developed machine learning (ML) approach to improve orbit prediction accuracy is systematically investigated using three ML algorithms, including support vector machine (SVM), artificial neural network (ANN), and Gaussian processes (GPs). In a simulation environment consisting of orbit propagation, measurement, estimation, and prediction processes, totally 12 resident space objects (RSOs) in solar-synchronous orbit (SSO), low Earth orbit (LEO), and medium Earth orbit (MEO) are simulated to compare the performance of three ML algorithms. The results in this paper show that ANN usually has the best approximation capability but is easiest to overfit data; SVM is the least likely to overfit but the performance usually cannot surpass ANN and GPs. Additionally, the ML approach with all the three algorithms is observed to be robust with respect to the measurement noise.
Similar content being viewed by others
Change history
11 February 2022
A Correction to this paper has been published: https://doi.org/10.1007/s42064-022-0136-2
Abbreviations
- RSO(s):
-
resident space object(s)
- SSO:
-
solar-synchronous orbit
- LEO:
-
low Earth orbit
- MEO:
-
medium Earth orbit
- SVM:
-
support vector machine
- ANN:
-
artificial neural network
- GPs:
-
Gaussian processes
- RSW:
-
local orbital frame (orthogonal axes along radial/along-track/cross-track directions respectively)
- e :
-
orbit prediction errors in RSW frame
- ex, ey, ez :
-
position components of e (km)
- evx, evy, evz :
-
velocity components of e (m/s)
- eζ :
-
a general reference to one of six components of e above
- eT :
-
vector of true prediction error
- eres :
-
vector of residual error
- êML :
-
vector of ML-predicted orbit prediction error
- P ML(eζ):
-
performance of the ML model on the component eζ
- m :
-
number of learning variables for ML models
- n :
-
number of data points in the training data
- k :
-
number of basis functions of GP models
References
Kelso, T. S. Iridium 33/Cosmos 2251 Collision. Information on http://celestrak.com/events/collision/ (cited 15 Feb 2017).
Abu-Mostafa, Y. S., Magdon-Ismail, M., Lin, H. T. Learning from Data. AMLBook, 2012.
Hartikainen, J., Seppänen, M., Särkkä, S. State-space inference for non-linear latent force models with application to satellite orbit prediction. In: Proceedings of the 29th International Conference on Machine Learning, 2012.
Ampatzis, C, Izzo, D. Machine learning techniques for approximation of objective functions in trajectory optimisation. In: Proceedings of the International Joint Conference on Artificial Intelligence 2009, Workshop on Artificial Intelligence in Space, 2009.
Sharma, S., Cutler, J. W. Robust orbit determination and classification: a learning theoretic approach. The Interplanetary Network Progress Report 42–203, 2015.
Barton, K. E., McLaughlin, C. A. Long short-term memory neural networks for the prediction of localized atmospheric density for orbit determination. In: Proceedings of 2018 AAS/AIAA Astrodynamics Specialist Conference, 2018.
Ertl, C. A., Christian, J. A. Identification of partially resolved objects in space imagery with neural networks. In: Proceedings of 2018 AAS/AIAA Astrodynamics Specialist Conference, 2018.
Parrish, N. L., Scheeres, D. J. Optimal low-thrust trajectory correction with neural networks. In: Proceedings of 2018 AAS/AIAA Astrodynamics Specialist Conference, 2018.
Smet, S. D., Scheeres, D. J., Parker, J. S. Systematic exploration of solar gravity driven orbital transfers in the Martian system using artificial neural networks. In: Proceedings of 2018 AAS/AIAA Astrodynamics Specialist Conference, 2018.
Jia, S. Y., Shan, J. J. Neural network-based adaptive sliding mode control for gyroelastic body. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(3): 1519–1527.
Xia, X., Jia, Y., Xu, S., Wang, X. An adaptive nonsingular terminal sliding mode tracking control using neural networks for space manipulators actuated by CMGs. In: Proceedings of 2018 AAS/AIAA Astrodynamics Specialist Conference, 2018.
Peng, H., Bai, X. L. Improving orbit prediction accuracy through supervised machine learning. Advances in Space Research, 2018, 61(10): 2628–2646.
Peng, H., Bai, X. L. Exploring capability of support vector machine for improving satellite orbit prediction accuracy. Journal of Aerospace Information Systems, 2018, 15(6): 366–381.
Peng, H., Bai, X. L. Artificial neural network-based machine learning approach to improve orbit prediction accuracy. Journal of Spacecraft and Rockets, 2018, 55(5): 1248–1260.
Peng, H., Bai, X. L. Gaussian Processes for improving orbit prediction accuracy. Acta Asstronautica, 2019, 161: 44–56.
Peng, H., Bai, X. L. Machine learning approach to improve satellite orbit prediction accuracy using publicly available data. The Journal of the Astronautical Sciences, 2019. https://doi.org/10.1007/S40295-019-00158-3.
Maisonobe, L., Pommier, V., Parraud, P. Orekit: An open source library for operational flight dynamics applications. In: Proceedings of the 4th International Conference on Astrodynamics Tools and Techniques, 2010.
Vapnik, V. N. The Nature of Statistical Learning Theory, 2nd edn. New York: Springer-Verlag New York, 2000.
Abu-Mostafa, Y., Magdon-Ismail, M., Lin, H. E. Chapter 8: Support Vector Machines. In: Learning from Data. AMLBook, 2012.
Steinwart, I., Christmann, A. Support Vector Machines. New York: Springer-Verlag New York, 2008.
Abu-Mostafa, Y., Magdon-Ismail, M., Lin, H. E. Chapter 7: Neural networks. In: Learning from Data. AMLBook, 2012.
Nielsen, M. A. Neural Networks and Deep Learning. Determination Press, 2015.
Du, K. L., Swamy, M. N. S. Neural Networks and Statistical Learning. London: Springer-Verlag London, 2014.
Murphy, K. P. Machine Learning: a Probabilistic Perspective. Cambridge: The MIT Press, 2012.
Almosallam, I. A., Jarvis, M. J., Roberts, S. J. GPz: Non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts. Monthly Notices of the Royal Astronomical Society, 2016, 462(1): 726–739.
Almosallam, I. Heteroscedastic Gaussian processes for uncertain and incomplete data. Ph.D. Dissertation. Oxford, Oxfordshire: University of Oxford, 2017.
Quinonero-Candela, J., Rasmussen, C. E. A unifying view of sparse approximate Gaussian process regression. Journal of Machine Learning Research, 2005, 6: 1939–1959.
Christopher, M. B. Pattern Recognition and Machine Learning. New York: Springer-Verlag New York, 2006.
Rasmussen, C. E., Williams, C. K. I. Gaussian Processes for Machine Learning. Cambridge: The MIT Press, 2005.
Peng, H., Bai, X. L. Generalization capability of machine learning approach among different satellites: validated using TLE data. In: Proceedings of 2018 AAS/AIAA Astrodynamics Specialist Conference, 2018.
Acknowledgements
The authors would acknowledge the research support from the Air Force Office of Scientific Research (AFOSR) FA9550-16-1-0184 and the Office of Naval Research (ONR) N00014-16-1-2729. Large amount of simulations of RSOs have been supported by the HPC cluster in School of Engineering, Rutgers University.
Author information
Authors and Affiliations
Corresponding author
Additional information
Hao Peng has been a postdoctoral associate at Rutgers University since August 2016. He received his Ph.D. degree of engineering in 2016 from Beihang University. His current study focuses on introducing machine learning, data mining, and artificial intelligence techniques into the aerospace field to solve previously seemingly impossible tasks. His research interests also include dynamical system theory, restricted three-body problem, space trajectory design, orbit control, and optimal control problems. Dr. Peng's academic activities are actively updated at https://SpaceResearch.top, Google Scholar, and Research Gate.
Xiaoli Bai has been an assistant professor in the Department of Mechanical and Aerospace Engineering at Rutgers University since July 2014. She obtained her Ph.D. degree of aerospace engineering in 2010 from Texas A&M University. One consequence of her dissertation is a set of methods which significantly enhances and accelerates the fundamental processes underlying the creation and maintenance of space debris catalogs. Her current research interests include astrodynamics and space situational awareness with a focus on the unstable and inactive space debris that are out of control and have uncertain origins; spacecraft guidance, control, and space robotics; and Unmanned Aerial Vehicle navigation and control. Dr. Bai was a recipient of Outstanding Young Aerospace Engineer Award from Texas A&M University in 2018, A. Water Tyson Assistant Professor Award from Rutgers in 2018, the 2016 Air Force Office of Scientific Research Young Investigator Research Program Award the American Institute of Aeronautics and Astronautics Foundation John Leland Atwood Graduate Award, and Amelia Earhart Fellowship. E-mail: xiadi.bai@rutgers.edu.
Rights and permissions
About this article
Cite this article
Peng, H., Bai, X. Comparative evaluation of three machine learning algorithms on improving orbit prediction accuracy. Astrodyn 3, 325–343 (2019). https://doi.org/10.1007/s42064-018-0055-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42064-018-0055-4