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    Averaging
    From: Alexandre Eremenko
    Date: 2004 Oct 6, 23:45 -0500

    Many manuals advise to take several sights
    in short sequence and then to average the result.
    and to reduce the average as one sight.
    (Chauvenet recommends at most 6, Russian manuals 3-5).
    The purpose is to increase accuracy,
    and, probably more importantly, to reject the sights
    with an evident "human error".
    
    Recently I was asked off-the-list by Bill Burchill,
    what is the effect of the motion of the vessel
    on these repeated sights
    (they are all taken from different positions!)
    
    As I did not find an answer in Bowdich (or Norie, or other manuals),
    I think this should be
    addressed in this list.
    
    My answer is a "theorist's" answer and I appreciate any
    CORRECTIONS BY MORE EXPERIENCED navigators.
    
    The short answer is this: don't bother about this, when sailing
    a sailboat or even an aircraft carrier.
    (However, I imagine that this recommendation has to be modified
    for a navigator of a strategic bomber flying at 600 knots.
    I don't know much about the aerial navigation, but I suppose
    it had to be done by cell nav before GPS era, and if you are over an
    ocean).
    
    So, suppose your vessel moves at 10 knots, (10nm/hour=(1/6)mile/min
    =10"/min),
    and you take 5 altitude sights with the interval
    of approx. 1 minute. Then the maximal change in the altitudes
    due to your motion will be of the order of 50", =approx 1'.
    Thus it seems that on such a small interval, all your
    altitudes (those taken correctly) will lie on a straight line
    when plotted against GMT.
    
    This justifies the recipe: take the average of your altitudes
    and the average of your GMT, and reduce these averages,
    and the resulting position line will pass through your place
    at the average observation time.
    
    What is probably done in practice, is first plotting
    your altitudes against GMT, then looking for a straignt
    line which passes most closely through MOST of your dots,
    then discarding those observations which are far away from
    this line (this rejects crude human eroor),
    then averaging the times and the altitudes of the rest,
    and reducing this average.
    
    This recipe should indeed increase the accuracy,
    reject the sights with large "human error", and thus
    be more precise and more reliable than a single observation.
    
    Unless you are on the strategic bomber mentioned above,
    in which case the recipe does not seem to be applicable.
    (I have never seen a strategic bomber (or commertial aircraft)
    navigators manuals).
    
    Alex.
    
    
    

       
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