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    Re: Cocked hats, again.
    From: Philip Bailey
    Date: 2007 Mar 15, 16:39 -0700

    > Gary LaPook wrote:
    > See my March 6th post.
    > You can draw circles around the fix plotted in the center of the
    > cocked hat of various radii to show the probabilities of your actual
    > position. When the triangle is small it may lie entirely inside a
    > particular probability circle, such as the CEP, so the portion inside
    > the circle but outside the triangle are possible positions. When the
    > triangle is very large all the probability circles will be contained
    > within the triangle so all positions must also be within the triangle.
    > This is an alternate way to describe the situations that I described
    > in my post of today, March 15th and illustrated in the diagrams.
    After looking back at Gary LaPook's March 6th post, I can see where he
    is coming from, and why he seems to be talking at cross purposes with
    George Huxtable and others.
    I (and perhaps others) thought that the following problem of
    estimating one's position was being discussed.  If not, perhaps it
    should be:
    (1) 3 celestially (or otherwise) obtained lines of position.
    (2) No systematic error--i.e. random error only.
    (3) Crucially here in this academic discussion, NO other data is
    Point (3) means that information such as standard deviations (SDs) is
    unavailable.  There is no means that I can see of calculating a SD
    from 3 LOPs.  One cannot therefore (in this discussion) draw a "CEP".
    Taking the latter out of the discussion may make it intuitively more
    obvious why, statistically, given 3 LOPs and no other data, why one's
    position is more likely to be outside the triangle than inside it.  A
    smaller triangle does then, in principle, shrink the possible area in
    which one may be, and a larger one indicate that the possible error of
    position is higher.
    In short, Gary should first address this simplified problem and
    disregard any other data he may have.
    In reality, at sea, one would not disregard other data, but surely
    actual, current, observations should be given much more weight than he
    Philip Bailey
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