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    Re: Symmedian point -earliest reference in navigation
    From: Brad Morris
    Date: 2018 Oct 15, 14:12 -0400
    Bill, you wrote

    I have searched through the NavList archives, I followed most of the references in David Burch's helpful blog post http://davidburchnavigation.blogspot.com/2016/07/most-likely-position-from-3-lops.html

    From David Burch Navigation

    Begin quote

    "Practicing navigators have tended to choose the best position within the triangle of intersecting LOPs (cocked hat) as some central value of their choice, based on their experience and the actual sights at hand. In most cases this is an adequate solution, but in rare cases ...

    ...It can be shown that if the standard deviations of the sights are all the same (no one LOP better than another), and there is no systematic error that applies to all of them, then the most likely position is located at what is called the symmedian point"

    End quote, emphasis added.


    By following this advice, we may "improve" our fix, but only under certain circumstances.  At the end of the geometric construction (or the matrix manipulations, if so inclined), the symmedian point is found.  It will likely be different from the "by eye" dot.  It will certainly be a different fix than that found by following Admiralty advice, particularly with danger nearby.

    Bill, please answer the following questions for practical navigators.

    1)  How are we to know, with certainty, that
        [a] the standard deviations of the sights are all the same, and 
        [b] there is no systematic error 
    Most importantly, the method by which we are to know.   Do you expect navigators to determine the statistical distribution of the observations of each body, so as to know that the standard deviations for each body are all the same?  

    2) Please justify why using the symmedian point is better than Admiralty advice on the cocked hat.  Or do you only recommend the symmedian point when there is no danger nearby and all of the conditions met?

    Aside from the pure exercise of applied mathematics, answering these questions should improve the focus and rationale for the symmedian point lecture.


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