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    Maximum likelihood position with triangle on a sphere
    From: Bill Lionheart
    Date: 2018 Oct 19, 17:09 +0100

    So now we all know the symmedian point (and I expect some of you are a
    bit fed up with it. Sorry!) For a plane triangle formed by three lines
    of position with the correct direction but zero mean normally
    distributed errors in the distances from the true position the maximum
    likelihood estimate is the symmedian point.
    
    I was thinking of related problems on the sphere. Some of which I can
    solve and some I don't know how to solve yet.
    
    For example suppose we have three great circle position lines with
    some sensible  assumption about the errors. For example radio
    direction finding from distant stations.
    
    Or three small circles, as we would get if we were using celestial
    navigation and had the altitude of three bodies, but the errors were
    huge so the straight line approximation was not valid.
    
    There is a definition of a symmedian point and a Lemoine point for a
    spherical triangle (but they are different). Of course I could compute
    a point numerically using an optimization code, but I am looking for
    geometric descriptions of the maximum likelihood estimate.
    
    My question is just if NavList members know of anything in the
    literature. (..public or secret).
    
    Thanks
    
    Bill Lionheart
    

       
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