A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Pike
Date: 2020 Jul 19, 00:48 -0700
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
I got as far as the bottom of the first page plus a quick scan of the diagrams before my head started to hurt. Thus proving I don’t have a ‘mathematical bent’. However, it seems to me that they’re trying to prove the blindingly obvious. After all, a three PL triangle converging to a single point is generally considered a good fix, but the chances of being in the centre of that tiny triangle much be close to zero.
I would have thought in these days of the digital computer that it ought to be possible to set up a trial with millions of fixes with the PLs generated randomly from each source, first with the sources for the same equipment with the same bands of error and the dame distance away. Then having seen what you got, you could use sources different distances away or with different band of error to see if you got a different result. After that you could try all sources on one side (i.e. 60 degree not 120 degree cut), perhaps with a bit of systematic error fed in. You might also like to look at the effects of quadrantal error with respect to receiver heading vs source relative bearings. It would be interesting to know which of these made much difference.
Alternatively, build up the vitamin D by getting out and taking a few real fixes outside. DaveP