Some of the most common metrics for collision risk assessment are the probability of collision, miss distance in Mahalanobis space, and confidence intervals. Sometimes they are used in combination; for example, the miss distance is used as a prescreening method to identify potentially hazardous conjunctions; other times they are used as alternative means; that is, covariance ellipse overlapping checks are employed instead of computing the probability of collision. In this work, we show that the three risk indexes are intimately connected once a suitable distance is defined. We argue that Mahalanobis miss distance is a proper metric only when the sigma-normalized hard-body size is negligible; we thus investigate the minimum Mahalanobis distance between the hard-body circle and the combined position covariance as an alternative. Its computation is fully analytic, as the most complex operation is finding the roots of a quartic polynomial. When multiplied by the sigma-normalized hard-body radius, such distance provides an upper bound to the collision probability. When used to scale the covariance matrix, it provides the largest confidence interval supporting a noncollision event. Finally, when adopted as an actionable threshold, analytical bounds on the probability of miss detection and of false alarms can be computed.


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    Titel :

    Relations Between Collision Probability, Mahalanobis Distance, and Confidence Intervals for Conjunction Assessment


    Beteiligte:
    Modenini, Dario (Autor:in) / Curzi, Giacomo (Autor:in) / Locarini, Alfredo (Autor:in)

    Erschienen in:

    Erscheinungsdatum :

    2022-03-11


    Format / Umfang :

    10 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




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