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SUMMARY:OPEN SOURCE ORBIT DETERMINATION WITH SEMI-ANALYTICAL THEORY
DTSTART;VALUE=DATE-TIME:20181107T133000Z
DTEND;VALUE=DATE-TIME:20181107T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T094936Z
UID:indico-contribution-3880@indico.esa.int
DESCRIPTION:Speakers: Luc Maisonobe (CS SI)\nSpace objects catalog mainten
ance demands an accurate and fast orbit determination (OD) process to cope
with the ever increasing number of observed space objects. The developmen
t of new methods\, that answer the two previous problems\, becomes essenti
al.\n\nPresented as an alternative to numerical and analytical methods\, t
he Draper Semi-analytical Satellite Theory (DSST) is an orbit propagator b
ased on a semi-analytical theory allowing to preserve the accuracy of a nu
merical method while providing the speed of an analytical method. This pro
pagator allows computing the mean elements and the short-period effects se
parately. We reproduced this architecture at the OD process level in order
to be able to return\, as desired\, the mean elements or the osculating e
lements. Two major cases of use are thus possible: fast OD for big space o
bjects catalog maintenance and mean elements OD for station keeping issues
.\n\nThis paper presents the different steps of development of the DSST OD
included in the Orekit open-source library. Integrating an orbit propagat
or into an OD process can be a difficult procedure. Computing and validati
ng derivatives is a critical step\, especially with the DSST whose equatio
ns are very complex. To cope with this constraint\, we used the automatic
differentiation (AD) technique. AD has been developed as a mathematical to
ol to avoid the calculations of the derivatives of long equations. This is
equivalent to calculating the derivatives by applying chain rule without
expressing the analytical formulas. Thus\, AD allows a simpler computation
of the derivatives and a simpler validation. AD is also used in Orekit fo
r the propagation of the uncertainties using the Taylor algebra.\n\nExisti
ng OD applications based on semi-analytical theories calculate only the de
rivatives of the mean elements. However\, for higher accuracy or if the fo
rce models require further development\, adding short-period derivatives i
mproves the results. Therefore\, our study implemented the full contributi
on of the short-period derivatives\, for all the force models\, in the OD
process. Nevertheless\, it is still possible to choose between using the m
ean elements or the osculating elements derivatives for the OD.\n\nThis pa
per will present how the Jacobians of the mean rates are calculated by AD
into the DSST-specific force models. It will also present the computation
of the state transition matrices during propagation. Both mean elements an
d short-periodic derivatives are developed. The performance of the DSST OD
is demonstrated under Lageos2 and GPS orbit determination conditions.\n\n
**Keywords**: Orbit determination\, Automatic differentiation\, Semi-analy
tical theory\, DSST\, Open-source\, Orekit.\n\nhttps://indico.esa.int/even
t/224/contributions/3880/
LOCATION: Single 107
URL:https://indico.esa.int/event/224/contributions/3880/
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