Because of the increasing number of objects in low Earth orbit, the fast and reliable estimation of the collision risk is an important challenge for spacecraft owners/operators. Among the available risk indicators, this paper focuses on computing the instantaneous probability of collision, which can be modeled as the integral of a three-dimensional Gaussian probability density function over a Euclidean ball. The authors propose an efficient and accurate method for evaluating this integral. It is based on the combination of two complementary strategies. For the first one, convergent series and numerical error bounds are computed. These bounds provide a tradeoff between the accuracy needed and the number of terms to compute. The second one, using divergent series, approximates the value of the integral with a good accuracy in most cases with only a few terms computed. Based on those two methods, a hybrid algorithm is tested on cases borrowed from the literature and compared against existing methods. Several numerical results and comparisons confirm both the efficiency and robustness of this paper’s approach.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Fast and Reliable Computation of Instantaneous Orbital Collision Probability


    Contributors:

    Published in:

    Publication date :

    2024-08-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Satellite Instantaneous Collision Probability Computation Using Equivalent Volume Cuboids

    Zhang, Shuo / Fu, Tuo / Chen, Defeng et al. | AIAA | 2020

    Free access

    FAST PROBABILITY-OF-COLLISION COMPUTATION

    GUPTA UJJWAL DAS / LESIV ROSTYSLAV / SAUND BRADLEY LARKIN et al. | European Patent Office | 2024

    Free access

    Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters

    Serra, Romain / Arzelier, Denis / Joldes, Mioara et al. | AIAA | 2016


    Computation of Orbital Conjunctions and Collision Prediction Methods

    Henderson, D. M. / AAS; Space Flight Mechanics Technical Committee| AIAA; Astrodynamics Technical Committee | British Library Conference Proceedings | 1999


    Mahalanobis Shell Sampling (MSS) Method for Collision Probability Computation

    Nunez Garzon, Ulises E. / Lightsey, E Glenn | AIAA | 2021