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At 11:50 01/05/02 -0400, Dov Kruger wrote:

>
>So, while he is thinking about the problem, in the meantime, he mentions
>a related unsolved problem just to show how "unsimple" this is:
>
>Consider a two-variable bivariate gaussian, (shooting at a target). For
>n shots, what is the distribution of the size of the smallest circle
>that can enclose all the points?
>This is an unsolved problem. It isn't trivial, and he therefore doubts
>that the navigation problem is any easier to come up with an analytical
>answer.
>

This measurement of group size by "extreme spread" is just one way of
measuring the size of a group. Its only virtue is that it is easy to
measure. But as Dov intimates, it is not an efficient way to measure group
size. For this reason, ordnance factories and ammunition makers do not use
this method for assessing the accuracy of their ammunition.

Nor do I think it is relevant to the cocked hat problem, since we are not
asking the question, "What size is the smallest circle that we can put
around a distribution of n cocked hats?"

The question (I think) we are asking is, "Given this distribution of n
cocked hats, where is the most probable position and what is the error in
its position?" This is a much more tractable problem.

Better yet to plot means for the multiple observations on each bearing and
then use the standard deviations to say something about the errors on each
mean and so to the error on the MPP. This is the most efficient way to
proceed.

Geoffrey Kolbe.

   

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