A Power Series Expansion based Method to compute the Probability of Collision for Short-term Space Encounters - Archive ouverte HAL Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2015

A Power Series Expansion based Method to compute the Probability of Collision for Short-term Space Encounters

Romain Serra
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Mioara Joldes
Bruno Salvy

Résumé

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.
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Dates et versions

hal-01131384 , version 1 (13-03-2015)
hal-01131384 , version 2 (23-03-2015)

Identifiants

  • HAL Id : hal-01131384 , version 2

Citer

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⟩
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