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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.
    2 LoP.png

    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
    Navigational Algorithms
    http://sites.google.com/site/navigationalalgorithms/

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