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    Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    From: George Huxtable
    Date: 2009 Apr 23, 15:33 +0100

    Brad wrote
    
    Gentlemen,
    
    -I originally proposed this "Prove It" method, so that I could discover the
    truth and cut through the hyperbole.
    
    We proposed a test, in which George would give several altitudes around
    noon, and each contributor would then calculate the noon fix (lat lon) from
    the given altitudes.
    
    At this juncture, we seem to be waiting for a data set to be present to Jim
    Wilson.  George, I urge you to complete that task so that we can see how a
    manually graphed method compares to the mathematically rigorous Excel least
    squares fit.
    
    We can see that the least squares fit certainly provides a fix much like
    Frank said it would.  That is, Frank indicated longitude to within 5 miles,
    and Dave got 5.68 miles.  Let us hope that there is no quibbling over 0.68
    miles.  I think for a least squares fit, we can convince ourselves as to the
    validity of the experiment.
    
    What remains then is the manual graphing or paper folding methods.  While we
    can expect some degradation in performance, I do not believe we are
    discussing wholesale failure.  Rather, there will be some variance from a
    rigorous curve fit to a mark-1 eyeball fit.  This can be debated endlessly,
    as to the performance of one individual or another.  However, it is my
    estimation that the fix will be within the ballpark, and the method
    "proven".
    
    I still want to see how Jim's method performs....
    
    =====================
    
    I concur with the thrust of Brad's message. When tested using  the full
    might of Excel's least-squares fitting, Frank's procedure performed
    significantly better than my expectation, and conformed reasoably well with
    the claims he had made for it.
    
    It's a pity that nobody has chosen, as yet, to apply his own hand and eye to
    a  graphing technique suitable for use onboard, which I expect would be
    somewhat degraded compared with the least-squares fit, though not a lot.
    
    Hewitt Schlereth has generated a set of random numbers which we haven't
    seen, and derived from them, using his own producedure, a result which he
    claims to be within 1' of the initial longitude. That is certainly possible,
    but a single result tells little about the scatter. Simple luck can cause
    your first shot at a dartboard to hit the bull's-eye. I ask Hewitt to deduce
    a few more sets of numbers, taken from the data set that I put out attached
    to [7940] as noon1a.rtf, or (the same data), attached to [7959], as
    noon1a.doc . I don't ask for all 20, but just a few, to get an idea of
    scatter. As for the principle of Hewitt's approach, it may indeed be the
    best, to work out the centre of symmetry before correcting for North-South
    speed, then allow for the effect of that speed afterwards.
    
    I expected it to be a simple matter to provide a set of tinkered data to
    meet Jim's needs, but is has proved a surprisingly awkward task. Dave Walden
    has kindly offered some help, so between us we may have some numbers to
    offer Jim very shortly. He is being very patient.
    
    Here's what I've tried to generate, for Jim, and he can say if it would meet
    his needs.
    
     I wanted to allow simulated data to be collected in a procedure that a real
    observer might follow, not allowing any foresight about what's coming next.
    
    What I proposed was to provide predictions at fixed times of
    12:10, 12:11, 12:12, 12:13; 12:14.
    then a gap until 12:35, 12:40, 12:45.
    Then keep predicting and noting (but not recording) altitudes over the next
    half-hour, at 1-minute intervals, looking out for the first moment that the
    predicted altitude falls below or equal to that made for 12:14. We can call
    that moment time T. Predictions made between 12:45 and time T are
    immediately discarded. Record time T and its altitude, and then record a
    further 4 altitudes. So the last batch of 5 is at -
    T, T+1, T+2, T+3, T+4.
    
    Then I would present Jim with a table with a table with 13 columns showing
    those 13 altitudes, similar to what went before, together with an additional
    column showing time T (the time that the observation in column 9 was taken),
    and another with an identifier code. Further columns showing assumed lat,
    long, and speed, including their scatter, will be retained, not disclosed
    until later, as we did before.
    
    My aim would be to put out no more than a page-full of stuff, say 20
    data-sets as before, enough to give a rough idea of scatter. I might expect
    that no more than a few of those 20 would be actually tackled by a graphical
    procedure.
    
    I strongly suspect that Jim's procedure, because it concentrates on the
    outer fringes of the timing, in which altitudes are more sensitive to
    hour-angle, could actually provide a marginal statistical improvement in
    determining longitude (not latitude) over the simpler equally-timed case.
    But it would be hard to detect marginal differences without lots of
    statistics.
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
    
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