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Subject: Re: On LOPs
From: Steven Tripp (tripp@XXX.XXX)
Date: Sun Apr 14 2002 - 23:07:47 EDT
On 4/13/02 9:18 PM, "Peter Fogg" <ffive@XXX.XXX> 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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