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Rodney Myrvaagnes wrote-

> 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.

George responds-

I have never said that, or anything like it. I don't know what Rodney means
by "locations that could give rise to those LOP's", or how those locations
could be determined.

At the risk of boring further those listmembers who have heard enough about
LOP's, let me copy out, once again, the  exact text of the contention I put
forward a month or so ago, which started this business off.

============
>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.
============

The simplest implementation to test this would be to tether one's vessel to
a well-charted beacon, in conditions when the sea is rough enough to
perturb the compass readings appreciably, in a Gaussian sort of way. Take a
round of bearings of three well-charted landmarks, And then another round.
And another. And so on.  Then, I contend, only one in four of the triangles
so formed will contain the true position.

That's all it will tell you. It doesn't even attempt to derive a
distribution of possible locations, that Rodney seems to be asking for.
That might indeed be useful, but it's not available.

So I ask Rodney and others to address themselves to the problem as stated.
If indeed they wish to set up another, quite different, hypothesis, in
order to shoot it down, I ask them to be quite clear, to themselves and to
us, that that is what they are doing.

George Huxtable.

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george@huxtable.u-net.com
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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