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    Re: Cocked hats, again.
    From: Peter Fogg
    Date: 2007 Mar 21, 02:35 +1100
    Yesterday I wrote:
    > If you can and want to, calculate the standard deviation of multiple sights and construct shadow position lines that will enclose about a 70% and then about a 90% chance that this larger shape encloses the position. 
    > This is, apparently, statistically quite valid and converts your allegedly 25% chance of the shape containing the position to a 70% or 90% chance. However the fix; the only indicative point of position that can be rationally derived, remains in the same place.

    Now it occurs to me that this "remains in the same place" is not necessarily correct. It would be for the standard deviation (deviation from an average) affecting all position lines, if calculated this way.

    However, if multiple sights leading to each position line were separately analysed, as with the slope technique, then a different standard deviation for each position line could be derived.

    In that case this diagram roughly sketched earlier could be indicative; the lower position line displays a smaller standard deviation, leading to a displacement of the fix if calculated from these shadow lines.

    In this example the displacement is fairly trivial and the fix derived from the shadow lines is still near the centre of the original shape. Would this always be true? I guess it depends on the comparative sizes of the shape and each averaged deviation. The larger the deviation the larger the displacement.

    If nothing else it emphasises an advantage of eliminating error at source. If gross random error is taken out, as it tends to be with use of the slope technique, then a smaller standard deviation, representing an average of residual error, is one result.

    This shape begs the question: why would the standard deviations be so small compared to the shape? Remember that the standard deviations are derived from random error. Perhaps there is also systematic error present ...

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