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    Re: On LOPs
    From: Steven Tripp
    Date: 2002 Apr 15, 12:07 +0900

    On 4/13/02 9:18 PM, "Peter Fogg"  wrote:
    > George Huxtable seems to have declared open season on navigational sacred
    > cows.
    > First it was the noon sight, now it seems to be the turn of the idea of
    > finding a
    > positive fix position within the confines of three intersecting LOPs.
    > 'Well, the meaningfulness of a "cocked hat", whether from land bearings or
    > astro sights, is frequently misunderstood. It's a surprising fact that no
    > matter how good the navigator, only one time in four will his cocked hat
    > embrace his actual position, which is three times more likely to lie
    > outside it. This is a universal truth, relying in no more than this
    > proposition: that each position line, being the best estimate that can be
    > made, is just as likely to lie to the left of the true position as to the
    > right. So it's a big fallacy to imagine that the true position must be
    > within the cocked hat. Instead of a probability of 100%, it will be just
    > 25%.'
    This is sort of correct.  There is a statistical method for calculating the
    confidence ellipse that surrounds the Most Probable Position.  The size of
    the ellipse depends in part on the angles that the three LOPs cross at.  I
    have a program which calculates the ellipse.
    I attach an example of a 95% confidence ellipse.  If the mail server allows
    attachments...if not, I'll place it on my www server.
    Steve Tripp


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