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    Re: Cocked hats, again.
    From: Peter Fogg
    Date: 2007 Mar 17, 07:05 +1100

    DW: "An attemp to summarize and establish consensus."
    1. The most likely location is the center of the cocked hat.
    2. The probability of being within the cocked hat is 25%.

    DW; one statement contradicts the other! The thing about the centre is not that it is the most likely location, it is this:
    It is the ONLY fix position that can be calculated.

    Let's say that you are terribly worried that your shape might not enclose the position (why, I'm not sure, although this assumption underlies this subject). So you decide to enlarge the shape by an equal amount applied to each position line, equal to one standard deviation. Now you have a larger triangle, and are assured that it contains the position by an increase of about 70%.

    Let's say you're still worried (oh yes, you're a determined worrier). So you increase the size of your shape by another same amount. Now you have an even bigger shape, and the assurance that, on average, 90% of the time this much larger shape contains the position.

    Phew! That's a relief. Now you can relax.

    Having relaxed, you then need to put all this work to some useful purpose. Oh yes, that's right, while all this worrying was going on the boat was proceeding on its merry way. You now need to run that (increasingly) old fix forward to establish what you REALLY want to know: where you are! and establish a DR that you can use for your next round of sights.

    And where is that fix?

    Why, its at the centre of all three of these increasingly large shapes that you have constructed, of increasingly larger dimensions! It has remained in exactly the same place!

    At this point you may (or may not) wonder why you went to the effort, since it has changed nothing in terms of your practical navigation.

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