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Journal articles
Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters
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.
Cited literature [22 references]
https://hal.archives-ouvertes.fr/hal-01132149
Contributor : Mioara Joldes <>
Submitted on : Monday, March 16, 2015 - 5:13:46 PM
Last modification on : Monday, December 14, 2020 - 5:24:05 PM
Long-term archiving on: : Sunday, September 13, 2015 - 10:35:35 PM
Contributor : Mioara Joldes <>
Submitted on : Monday, March 16, 2015 - 5:13:46 PM
Last modification on : Monday, December 14, 2020 - 5:24:05 PM
Long-term archiving on: : Sunday, September 13, 2015 - 10:35:35 PM
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CollisionProbability.pdf
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