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    More Cocked Hats
    From: Bill Lionheart
    Date: 2020 Jul 18, 08:59 +0100

    NavList members with a mathematical bent might be interested in the
    latest thoughts on cocked hats from mathematicians.  Bárány, Steiger
    and Toledo https://arxiv.org/abs/2007.06838
    From the paper "The property that we are interested in is the
    probability of the cockedhat containing the true position being 1/4.
    Under what conditions is
    this statement true?"
    "Our aim in this paper is to show that the 25%-probability result is
    valid only for error distributions that guarantee that the three rays
    intersect at three distinct points and form a triangle.
    We note that the use of the cocked hat in navigation is today obso-
    lete, having been replaced by estimation of confidence regions, usually
    circles or ellipses, by computer algorithms."
    I would emphasize that this paper concerns "rays",, ie half a line. It
    is about cocked hats for position fixes taking bearings on objects in
    plane navigation.
    So, just in case anyone was still arguing in the pub about the 1/4
    probability after a navigation class maybe Bárány, Steiger and Toledo
    have the last word?

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