Speaker
Dr
Juan Félix San-Juan
(Scientific Computing Group (GRUCACI), University of La Rioja)
Description
The propagation of an orbit which is subject to perturbation forces is a non-integrable 6-degree-of-freedom problem that has been classically tackled in three different ways. General Perturbation Theories attempt to deduce an analytical expression for the future position and velocity of the orbiter as a function of its initial conditions and time. Nevertheless, the non-integrability of the problem makes it necessary to consider simplified models for the perturbing phenomena, as well as certain approximations that have a negative effect on long-term accuracy.
Another classical approach, Special Perturbation Theories, consist in applying numerical integration methods to the problem, which allows for the consideration of very complex mathematical models of perturbing phenomena. Nevertheless, in order to obtain highly accurate results, small integration steps must be taken, which implies long computational time.
The third way to handle the problem, Semi-analytical techniques, apply analytical transformations so as to remove the short-period dynamics from the equations of motion, which can be numerically integrated then through longer integration steps, and hence more reduced computational time. By doing so, long-term propagation can be performed very efficiently. Short-period dynamics can be recovered at the final epoch in order to complement the propagated mean elements and thus provide the osculating elements.
More recently, we have proposed a new approach, Hybrid Perturbation Theories, which consist of an integration method followed by a forecasting technique. The former, which can be any of the aforementioned techniques, is intended to generate an initial approximation, whereas the latter, which might be a statistical time series model or computational intelligence method, complements that approximation by forecasting its error at the final epoch. In order to achieve it, the second stage must model the dynamics corresponding to the difference between the output of the first stage and the real behaviour of the orbiter. An initial control period containing such dynamics is, therefore, necessary.
We will consider a hybrid propagator composed of SGP4 plus an additive Holt-Winters method in order to describe this methodology and the software it involves.
| Applicant type | First author |
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Primary author
Dr
Juan Félix San-Juan
(Scientific Computing Group (GRUCACI), University of La Rioja)
Co-authors
Dr
Iván Pérez
(Scientific Computing Group (GRUCACI), University of La Rioja)
Dr
Montserrat San-Martín
(Scientific Computing Group (GRUCACI))
Dr
Rosario López
(Center for Biomedical Research (CIBIR), Scientific Computing Group (GRUCACI), University of La Rioja)
