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    Re: Still on LOP's
    From: Rodney Myrvaagnes
    Date: 2002 May 3, 00:01 -0500

    If that is indeed the question, most of the argument has been off the
    point. I thought George was maintaining that no cocked hat that could
    arise from 3 LOPs with whatever error distribution could enclose more
    than 25% of the locations that could give rise to those LOPs. Even one
    counterexample defeats that claim, so maybe he is claiming something
    else.
    
    I can give lots of counterexamples. Another one herewith:
    
    An equilateral triangle of equivalent readings, with each vertex at the
    .1 distance (.1 probability of the reading being at that or greater
    distance) produces a probability of the location falling inside of 0.9
    * 0.9 * 0.9 =0.73, so 73% of locations will be inside. the triangles
    adjacent on each side will be inside 2 of the .9 bands, so will have a
    probability less than 0.9 * 0.9 * 0.1 <= .081 so less than 8% in those
    areas. The next triangles have 0.9 * 0.1 * 0.1 <= 0.009 or less than
    1%.
    
    The probability of that set of readings actually occurring is very low,
    but not zero.
    
    On Thu, 2 May 2002 08:59:04 +0100, Dr. Geoffrey Kolbe wrote:
    
    >
    >The question (I think) we are asking is, "Given this distribution of n
    >cocked hats, where is the most probable position and what is the error in
    >its position?" This is a much more tractable problem.
    >
    >Better yet to plot means for the multiple observations on each bearing and
    >then use the standard deviations to say something about the errors on each
    >mean and so to the error on the MPP. This is the most efficient way to
    >proceed.
    >
    
    
    Rodney Myrvaagnes                                  J36 Gjo/a
    
    
    "Curse thee, thou quadrant. No longer will I guide my earthly way by thee."  Capt. Ahab
    
    
    

       
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