NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
More Cocked Hats
From: Bill Lionheart
Date: 2020 Jul 18, 08:59 +0100
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 We note that the use of the cocked hat in navigation is today obso- lete, having been replaced by estimation of confidence regions, usually circles or ellipses, by computer algorithms."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? Bill
