Skip to Main content Skip to Navigation

A Power Series Expansion based 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 under Gaussian-distributed uncertainty. In this model of conjunction, classical assumptions reduce the probability of collision to the integral of a two-dimensional Gaussian probability density function over a disk. The computational method presented here is based on an analytic expression for the integral, derived by use of Laplace transform and D-finite functions properties. The formula has the form of a product between an exponential term and a convergent power series with positive coefficients. Analytic bounds on the truncation error are also derived and are used to obtain a very accurate algorithm. Another contribution is the derivation of analytic bounds on the probability of collision itself, allowing for a very fast and - in most cases - very precise evaluation of the risk. The only other analytical method of the literature - based on an approximation - is shown to be a special case of the new formula. A numerical study illustrates the efficiency of the proposed algorithms on a broad variety of examples and favorably compares the approach to the other methods of the literature.
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download
Contributor : Mioara Joldes <>
Submitted on : Monday, March 23, 2015 - 6:59:17 PM
Last modification on : Thursday, March 5, 2020 - 3:08:03 PM
Document(s) archivé(s) le : Monday, April 17, 2017 - 9:47:18 PM


Files produced by the author(s)


  • HAL Id : hal-01131384, version 2


Romain Serra, Denis Arzelier, Mioara Joldes, Jean-Bernard Lasserre, Aude Rondepierre, et al.. A Power Series Expansion based Method to compute the Probability of Collision for Short-term Space Encounters. [Research Report] LAAS-CNRS. 2015. ⟨hal-01131384v2⟩



Record views


Files downloads