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Probabilistic data association: the orbit set

Pirovano, Laura and Santeramo, Daniele A. and Armellin, Roberto and Di Lizia, Pierluigi and Wittig, Alexander Probabilistic data association: the orbit set. (2020) Celestial Mechanics and Dynamical Astronomy, 132 (2). ISSN 0923-2958

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Official URL: https://doi.org/10.1007/s10569-020-9951-z

Abstract

This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits—namely the orbit set—that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus allowing for a compact analytical description of the orbit set. The automatic domain splitting tool controls the truncation error of the polynomial approximation by patching the uncertainty domain with different polynomial expansions, effectively creating a mesh. The algorithm is tested for different observing strategies to understand the working boundaries, thus defining the region for which the admissible region is necessary to extract meaningful information from observations and highlight where the new method can achieve a smaller uncertainty region, effectively showing that for some observing strategies it is possible to extract more information from a tracklet than the attributable. Consequently, the method enables comparison of orbit sets avoiding sampling when looking for correlation of different observations. Linear regression is also implemented to improve the uncertainty estimation and study the influence of the confidence level on the orbit set size. This is shown both for simulated and real observations obtained from the TFRM observatory.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Politecnico di Milano (ITALY)
Other partners > University of Southampton (UNITED KINGDOM)
Other partners > University of Surrey (UNITED KINGDOM)
Laboratory name:
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Deposited On:13 Jan 2021 13:25

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