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George, I think you need to do better. The probability of the true
position lying on a measured LOP is higher than it is on either side,
not zero (Newton and Leibnitz took care of that when they invented
calculus).

If you want to simplify a normal distribution, a triangle would be a
better approximation than two squares. And, to avoid cluttering the
problem with intercepts, assume LOPs from bearings, rather than sextant
sights.

The width of the distribution, whether gaussian or triangle, must
overlap those from the other sights, and, if the three sights are
similar in difficulty, the width of the distribution should be the same
for all of them.

Even if you use your rectangular distributions, they overlap only at a
point inside the cocked hat at the narrowest possible size. Since the
cocked hat is itself your only measure of the error width, that is as
far as you need to go. Ergo, the way we have been doing it is correct.


On Thu, 18 Apr 2002 20:45:30 +0100, George Huxtable wrote:

>
>Well, I must admit to getting some enjoyment from confounding the
>conventional wisdom, but it is not entirely mischief-making. There are many
>navigators around who firmly believe that when they draw a cocked hat,
>their true position must lie inside it. If they can be convinced of the
>truth, that the true position is three times more likely to be outside the
>triangle than inside it, they will reinterpret their plots with greater
>understanding. And that can only do good.
>
>B

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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