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Trevor wrote:

> But, unless I am mistaking something (which is by no means
> impossible!), the probability that the cocked hat lies over the true
> position is numerically equal to the probability that that true position
> lies within the cocked hat.

From the point of view of probability theory, it is precisely the probability
that the cocked hat lies over the true position that we are talking about. All
the uncertainty lies in the measurements and plots of the bearings and hence in
the resulting cocked hat.  There is no uncertainty in the true position, only in
our knowledge of the true position, as represented by the cocked hat.

Trevor then went on to mention "the best estimate of the MPP".  Even if we grant
that the probability is 0.25 that the cocked hat lies over the true position, I
would argue that the Most Probable Position (MPP) is still the center of the
cocked hat.  Notice that the various possible cocked hats in Geoffrey's diagram
lie symmetrically about the true position. Even if you believe (with probability
0.75) that your particular cocked hat does not contain the true position, you
have no idea in which direction the true position lies relative to your cocked
hat, so you can do no better than select the center of your cocked hat as the
best estimate of your position given available information.  Can anyone refute
that argument?

Chuck Taylor
Everett, WA, USA

   

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