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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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