# NavList:

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

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Re: Ellipse of Confidence in position finding
From: Andrés Ruiz
Date: 2019 Mar 11, 09:15 +0100
Bill you wrote http://fer3.com/arc/m2.aspx/An-analytical-solution-two-star-sight-problem-celestial-Lionheart-mar-2019-g44520

Yes, I got "Numerical Methods in Matrix Computations", is a very good reference.
There, Theorem 2.1.1
m = number of sights and n = 2

Of course 1 LoP, the fix by 2 LoP could be in error.

How to define for them the EoC?
Infinite solutions. But we want only one.

I try to explain it.
To draw a circle in a paper, you need 3 restrictions. Like in a 2D CAD program. A circle is a special case of an ellipse.
It is a 2D problen with 3 DOF, degrees of freedom
1- pin the fist point of the circle -> the circle can rotate around this pin (now we have 2 DOF)
2- pin a different second point of the circle -> it can rotate through the center through the two fixed points (now we have 1 DOF)
3 - pin the 3rd point ->  No DOF, fixed circle.

Another important thing about ellipses. Remember my post with an example where the EoC, the symmedian point, and others give us the wrong position.
Fix by bisectors

Regards
--
Andrés Ruiz

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