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A New Method to Compute the Probability of Collision for Short-term Space Encounters

Romain Serra 1 Denis Arzelier 1 Mioara Joldes 1 Jean-Bernard Lasserre 1 Aude Rondepierre 2 Bruno Salvy 3
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
3 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This article provides a new method for computing the probability of collision between two spherical space objects involved in a short-term encounter. In this specific framework of conjunction, classical assumptions reduce the probability of collision to the integral of a 2-D normal distribution over a disk shifted from the peak of the corresponding Gaussian function. Both integrand and domain of integration directly depend on the nature of the short-term encounter. Thus the inputs are the combined sphere radius, the mean relative position in the encounter plane at reference time as well as the relative position covariance matrix representing the uncertainties. The method presented here is based on an analytical expression for the integral. It has the form of a convergent power series whose coefficients verify a linear recurrence. It is derived using Laplace transform and properties of D-finite functions. The new method has been intensively tested on a series of test-cases and compares favorably to other existing works.
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Conference papers
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https://hal.inria.fr/hal-01092420
Contributor : Bruno Salvy <>
Submitted on : Monday, December 8, 2014 - 4:28:26 PM
Last modification on : Friday, June 25, 2021 - 3:40:05 PM

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Romain Serra, Denis Arzelier, Mioara Joldes, Jean-Bernard Lasserre, Aude Rondepierre, et al.. A New Method to Compute the Probability of Collision for Short-term Space Encounters. AIAA/AAS Astrodynamics Specialist Conference, Aug 2014, San Diego, United States. 6p., ⟨10.2514/6.2014-4366⟩. ⟨hal-01092420⟩

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