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On Sun, 28 Apr 2002 12:44:54 +1000, Peter Fogg wrote:

>
>The really interesting thing, if this is correct, is that the fix position in the
>centre (centre in the sense of least squares) is exactly the same as from the
>smaller hat which has the same proportions. The only difference seems to be in the
>likelihood of the hat containing the AP: from 25%, according to the theory being
>examined, to 80% or 90%.
>
It is certainly true that a family of similar triangles could be
constructed, all parallel to an observational cocked hat, with the
sides all displaced equally, such that a trangle could enclose any
percent probablility of the actual location.

A set of observations could occur that would result in any triangle in
the family. Thus, the cocked hat resulting from three observations
could have any probablility between 0 and 1 of containing the true
position.

If the size of the triangle is used as evidence of the probable error
of the observations, which a reasonable navigator would do, then some
probability of the true result lying within the triangle could stay
constant for all cocked hats. This would depend on the distribution
function (gaussian would be reasonable) and could come out to 25% if
someone worked it out. Nobody has done so on this list AFAIK.




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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