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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

    Andrés Ruiz
    Navigational Algorithms


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