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    Re: Averaging
    From: Alexandre Eremenko
    Date: 2004 Oct 22, 12:45 -0500

    Dear Jim,
    Here are my comments on your summary:
    
    On Fri, 22 Oct 2004, Jim Thompson wrote:
    
    > So, is this a fair summary?
    >
    > Sextant sights are subject to a variety of errors,
    > leading to imprecision
    > and inaccuracy. One way to deal with random
    > observational error is to
    > average a set of several sights, and then
    > reduce and plot the average time
    > and altitude.
    >
    > Always apply basic principles to a run of sights:
    >
    > 1. Use only sights taken within a few minutes,
    > a minute or less between
    > sights.
    
    > 2. Use either the raw sextant observations,
    > or reduce each observation and
    > use the reduced set.
    
    If you reduce each observation, there is no point
    in averaging them.
    And there is no point in taking them in a short time
    interval.
    
    > observations. This elimates variation owing to the way
    > the corrections
    > themselves might vary, but it still does not
    > make the run of sights linear.
    
    The non-linearity question is relevant ONLY if you average row
    observations.
    
    > 1. The body is very likely to be changing
    > altitude in a nonlinear fashion.
    
    Just vice versa: very UNLIKELY.
    Namely: ONLY when near the meridian on high altitude.
    In all other cases it is linear for all practical purposes.
    
    > 2. High vessel speed can also lead to non-linearity in the data.
    
    No, it cannot. This was the subject of my very first
    message in this Averaging discussion, and everyone seemed
    to agree. It is only on jet-propulsion airplanes
    that the speed of the vessel can cause any noticeable
    non-linearity problem.
    
    
    

       
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