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    Re: Rejecting outliers
    From: George Huxtable
    Date: 2011 Jan 8, 14:10 -0000

    In his computer analysis of the data set that had been provided by Peter
    Fogg, I had questioned the freedom that Peter Hakel allowed for its slope
    to be determined from the data, when it was already predetermined from
    known information
    ----------------------------------------------------------------------------------------
    
    and Peter Hakel responded-
    
    "In some cases yes, but perhaps not all.  Answering your question would
    require me to simply repeat what I had written earlier about bad weather, position
    tracking vs. position determining, getting a good quality data set later in
    better conditions, etc.  I also said that I have no problem with precomputing
    the slope; I was simply interested in developing a useful tool that deals
    with the problem of sight averaging from a slightly different starting point.  I
    cannot think of adding anything else that would explain my motivation better.
    Given enough time, navigators can process their data by several methods and
    decide in the end with what result they feel most comfortable with.  Having
    a choice in that regard is not a bad thing."
    
    Yes, I agree with Peter about all of that...
    
    ============
    
    "It seems to me, however, that your well-known skepticism is applied
    inconsistently in this case. On the one hand you object to rejecting data
    points that don't seem to belong (by common-sense visual inspection, like Peter
    Fogg does), while on the other you are OK with constraining data set to a
    predetermined trend (slope) by trusting the DR (common sense in SOME
    cases).  I thought your skepticism would lead you to join me in asking: "What if, in
    this case, the DR is not quite reliable?  What useful processing can we do with
    this data then?"  It appears that I was wrong on that account."
    
    My "well-known skepticism" remains undimmed, I hope. I was most sceptical
    about the use, in Peter's computer analysis, of a slope of 24' (over 5
    minutes of time) deduced from a short sequence of highly-scattered data.
    Indeed, there was so much scatter in it that a slope of 32' was,
    statistically speaking, perfectly compatible with that set, if a somewhat
    worse fit than the 24', deduced and employed in Peter Hakel's analysis. Is
    Peter prepared to defend his value against the other?
    
    I pointed to the details of the observation that was made, because it tells
    us (unless there was some major error as yet undisclosed, which is always
    conceivable) that indeed 32' was the known, correct, slope, and the slope
    of 24' which Peter Hakel derived from that data and used in his analysis
    was simply way-out from that truth. Peter Fogg's data provides a good
    example of a case where precalculating slope can be useful.
    
    Under other conditions, a different situation might well arise, in which a
    very uncertain DR generates greater uncertainties in precalculating a slope
    than does the observed trend of altitudes, and perhaps Peter Hakel and I
    might agree that one should choose the most appropriate method depending on
    the circumstances.
    
    The logical flaw in any procedure that uses a predetermined slope as an
    important factor in a data analysis is that it first has to ASSUME an
    observer's position, when the end-result of the operation is to DETERMINE
    the observer's position. The get-out, from this catch, is that usually the
    geometry is such that even a very uncertain DR does not greatly perturb the
    slope, though this isn't always the case. A second get-out is that the
    problem can, if necessary, be treated as an iteration, though that may be
    taking such matters over-seriously.
    
    A simpler alternative is just to work with simple mean-values, of time and
    altitude, which together give a result independent of any slope.
    
    George.
    

       
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