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.
Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters
Journal of Guidance, Control, and Dynamics ; 39 , 5 ; 1009-1021
01.05.2016
Aufsatz (Konferenz) , Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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