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Brian Whatcott wrote:
Measure the length of the longest side of the cocked hat.
Use that as radius from the MPP in the cocked hat's interior  to draw a circle
for a circular estimate of position.

I suggest that has a reasonable chance of  in fact covering the
actual position. I think it puts the actual position in the circle, more often
than not.
?

An even simpler strategy might be to extend the LOPs out - as in away from their
intersections with other LOPs, by the same amount, and parallel to the original
LOP. As to the Maths involved I'm just guessing, but if they were each extended 10
miles or more outwards, would the likelihood of the Actual Position (AP) being
within this greatly larger cocked hat be something like 80% or 90%?

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%.

I think this is another version of my earlier 'smudged lines'.

   

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