# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: The Darn Old Cocked Hat vs CG?
From: Andrés Ruiz
Date: 2013 Mar 19, 19:59 +0100
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.

Regards

2013/3/19 Hanno Ix

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.

Regards

h

To: hannoix---net
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 = 0.0011
sigma = 1.3999
sigmaB = 1.0029
sigmaL = 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

--
Andrés Ruiz
Attached File:

View and reply to this message: http://fer3.com/arc/m2.aspx?i=122954

View and reply to this message: http://fer3.com/arc/m2.aspx?i=122955

--
Andrés Ruiz
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