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    Re: Avoiding the symmedian (and other) points
    From: Bill Lionheart
    Date: 2018 Nov 7, 06:05 +0000

    > A serious problem with the history of the computation of error ellipses was 
    a choice made by the editors at the Nautical Almanac office years ago. Around 
    the same time that the least squares solution started to be published 
    regularly in the Nautical Almanac itself (after 1989), a volume was published 
    covering a variety of calculation methods including the calculation of error 
    ellipses. Unfortunately they chose to calculate the standard deviation of the 
    observations from the observed sights themselves. This is an option but it 
    meant that error ellipses were undefined for a pair of lines of position, and 
    it implied certain other oddities. For example, a larger triangle for three 
    crossing lines automatically yielded a larger error ellipse. This apparently 
    satisfied the preconceived notions of navigation lore, but it was a poor 
    choice in mathematical terms. The standard deviation of observations should 
    be estimated a priori. Then two sights have an error ellipse that means 
    somethings. And also three sights have an error ellipse that does not 
    misleadingly shrink when the lines of position cross in a tiny triangle.
    >
    
    That is an interesting point Frank and gets to the origin of the
    confusion.  Was there a specific methodology published (eg in the
    Nautical Almanac) for estimating the standard deviation of the sights
    from the residual error?
    
    Bill
    

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