A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Brad Morris
Date: 2013 Mar 19, 15:14 -0400
This past weekend, Alex Eremenko and I visited with Frank Reed. In conversation, he lauded the error ellipse model as the best candidate for fix and confidence.
I do hope that I did understand Frank properly, and if not, I'm not trying to put words in his mouth.
I have a basic question for you. Is the MPP in your model compatible with Jim Wilson's MPP? Are they in general agreement? Jim's model, at least to this student, appears to offer a strong candidate for MPP which your confidence ellipse model then refines. Do I have this all wrong?
Hello Hanno,You wrote: Is there an counter example, one in which my choice of the TL would be far outside that ellipse?..No the fix is the MPP, most probable position, and the ellipse of confidence is centered on it. Why?, because is based in real observations, no random data. With an associated probability to be inside proportional to the area of the ellipse and inversely to the number of observations.In your random model the high prob is near the true position, but a priori is not known.And I insist each theoretical model must be validated against real data.Regards2013/3/19 Hanno Ix <hannoix---net>Andres:My rough-and-ready approach predicts the TL 2/3 down the median
as seen from the vertex (iow: at the CG) which it is - or at least rather close.In your diagram, it certainly is within the 99% ellipse.Could this be just a random coincidence?Is there an counter example, one in which my choice of the TL would be far outside that ellipse?If it is not by coincidence then the probability of its being within the Doch must be bigh.
From: Andrés Ruiz <navigationalalgorithms---com>
Sent: Tuesday, March 19, 2013 6:59 AM
Subject: [NavList] Re: Cocked hat vs Confidence ellipse
An example for 4 LoPs: see the attached animation for the ellipse of conficence of 25% 50% 75% 95% and 99% prob.Error:S = 0.0011sigma = 1.3999sigmaB = 1.0029sigmaL = 1.0499
Ellipse: Prob = 0.01 0.25 0.5 0.75 0.95 k = 0.1418 0.7585 1.1774 1.6651 2.4477 theta = 40.0289 40.0289 40.0289 40.0289 40.0289 a = 0.1637 0.876 1.3598 1.9231 2.8269 b = 0.1248 0.6675 1.036 1.4652 2.1539--
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