Abstract
A hybrid orbit propagator based on the analytical integration of the Kepler problem is designed to determine the future position and velocity of any orbiter, usually an artificial satellite or space debris fragment, in two steps: an initial approximation generated by means of an integration method, followed by a forecast of its error, determined by a prediction technique that models and reproduces the missing dynamics. In this study we analyze the effect of slightly changing the initial conditions for which a hybrid propagator was developed. We explore the possibility of generating a new hybrid propagator from others previously developed for nearby initial conditions. We find that the interpolation of the parameters of the prediction technique, which in this case is an additive Holt-Winters method, yields similarly accurate results to a non-interpolated hybrid propagator when modeling the \(J_2\) effect in the main problem propagation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
References
Akima, H.: A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Trans. Math. Softw. 4(2), 148–159 (1978)
Akima, H.: Algorithm 761: scattered-data surface fitting that has the accuracy of a cubic polynomial. ACM Trans. Math. Softw. 22(3), 362–371 (1996)
Akima, H., Gebhardt, A., Petzold, T., Maechler, M.: akima: interpolation of irregularly and regularly spaced data. R Foundation for Statistical Computing (2015). http://CRAN.R-project.org/package=akima, R package version 0.5-12
Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5), 1190–1208 (1995)
Pérez, I., San-Juan, J.F., San-Martín, M., López-Ochoa, L.M.: Application of computational intelligence in order to develop hybrid orbit propagation methods. Math. Probl. Eng. Article ID 631628, 11 (2013)
R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2015). https://www.R-project.org
San-Juan, J.F., San-Martín, M., Pérez, I.: An economic hybrid \(J_2\) analytical orbit propagator program based on SARIMA models. Math. Probl. Eng. Article ID 207381, 15 (2012)
San-Juan, J.F., San-Martín, M., Pérez, I., López, R.: Hybrid perturbation methods based on statistical time series models. Adv. Space Res. 57(8), 1641–1651 (2016). Advances in Asteroid and Space Debris Science and Technology - Part 2
Shanno, D.F.: Conditioning of quasi-Newton methods for function minimization. Math. Comput. 24(111), 647–656 (1970)
Winters, P.R.: Forecasting sales by exponentially weighted moving averages. Manage. Sci. 6(3), 324–342 (1960)
Acknowledgments
This work has been funded by the Spanish State Research Agency and the European Regional Development Fund under Project ESP2016-76585-R (AEI/ERDF, EU). Support from the European Space Agency through Project Ariadna Hybrid Propagation (ESA Contract No. 4000118548/16/NL/LF/as) is also acknowledged.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Pérez, I., San-Martín, M., López, R., Vergara, E.P., Wittig, A., San-Juan, J.F. (2017). Forecasting Satellite Trajectories by Interpolating Hybrid Orbit Propagators. In: Martínez de Pisón, F., Urraca, R., Quintián, H., Corchado, E. (eds) Hybrid Artificial Intelligent Systems. HAIS 2017. Lecture Notes in Computer Science(), vol 10334. Springer, Cham. https://doi.org/10.1007/978-3-319-59650-1_55
Download citation
DOI: https://doi.org/10.1007/978-3-319-59650-1_55
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59649-5
Online ISBN: 978-3-319-59650-1
eBook Packages: Computer ScienceComputer Science (R0)