Hybrid Analytical-Statistical Models

  • Juan Félix San-Juan
  • Montserrat San-Martín
  • David Ortigosa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6783)


To carry out new families of hybrid analytical orbit propagator programs a new methodology is presented. These families combine a simplified analytical orbit propagator with statistical time series models. In fact, this approach allows the increase of accuracy without loss of efficiency in the hybrid propagators as well as integrating the effects of those perturbations that have not been taken into account in the development of the analytical theory. These types of propagators can become, among other uses, good candidates for forming part of an economic onboard orbit determination system.


Analytical theory time series analysis hybrid-AOPP computer algebra 


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  1. 1.
    Brouwer, D.: Solution of the Problem of Artificial Satellite Theory Without Drag. Astron. J. 64, 379–397 (1959)MathSciNetGoogle Scholar
  2. 2.
    Hoots, F.R., Roehrich, R.L.: Spacetrack Report #3: Models for Propagation of the NORAD Element Sets, U.S. Air Force Aerospace Defense Command, Colorado Springs, CO (1980)Google Scholar
  3. 3.
    San-Juan, J.F.: Manipulación algebraica de series de Poisson. Aplicación a la teoría del satélite artificial. Ph.D. dissertation, Universidad de Zaragoza, Spain (1996)Google Scholar
  4. 4.
    San-Juan, J.F.: ATESAT: review and improvements. Study of a family of analytical models of the artificial satellite generated by ATESAT and their numerical validation versus PSIMU and MSLIB. Technical Report No. DGA/T/TI/MS/MN/97-258, CNES France (1998)Google Scholar
  5. 5.
    Box, G.E.P., Jenkins, G.M.: Time Series Analysis: forecasting and control. Holden-Day, San Francisco (1976)zbMATHGoogle Scholar
  6. 6.
    Deprit, A.: Canonical transformations depending on a small parameter. Celes. Mech. & Dynam. Astron. 1(1), 12–30 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    San-Juan, J.F.: ATESAT: Automatization of theories and ephemeris in the artificial satellite problem. Tech. rep. CT/TI/MS/MN/94-250, CNES France (1994)Google Scholar
  8. 8.
    San-Juan, J.F., López, L.M., López, R.: MathATESAT: A Symbolic-Numeric Environment in Astrodynamics and Celestial Mechanics (in preparation)Google Scholar
  9. 9.
    Mélard, G.: A Fast Algorithm for the Exact Likelihood of Autoregressive-moving. Applied Statistics 33, 104–114 (1984)CrossRefzbMATHGoogle Scholar
  10. 10.
    Jarque, C., Bera, A.: Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters 6, 255–259 (1980)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ljung, G., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrica 65, 297–303 (1978)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Juan Félix San-Juan
    • 1
  • Montserrat San-Martín
    • 1
  • David Ortigosa
    • 1
  1. 1.Departamento de Matemáticas y ComputaciónUniversidad de La RiojaLogroñoSpain

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