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Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
From: George Huxtable
Date: 2009 Apr 26, 10:48 +0100

```Some comments on Jim's thoughtful posting, about applying his "slope"
procedure to simulated data sets. It's been instructive, to him and to me;
perhaps to others.

If we can agree on what to do as a next-try, I will present his data as
degrees and decimal minutes.

He seems to be finding that he needs a longer observation period than 1 hour
to handle this situation. Of course, spreading over a longer time will
certainly improve precision, but moves us still further away from the
"around-noon" claim. I wonder if we can agree on some way to modify the
data-taking to suit Jim's needs better, while keeping within the bounds of
the claim, made originally by Frank Reed, that an hour's worth of
observations can produce longitudes within a scatter of +/- 5 miles rms, by
graphical means. That claim hasn't yet been tested, except in a limited
number of cases by Hewitt Schlereth, which will be discussed below. If Jim
thinks those boundaries have to be relaxed in some way, such as by extending
the job to 80 minutes rather than an hour, I will go along (with only slight
reluctance).

For this example, with its unsharp peak, would it perhaps be useful to
spread the "wing" observations for slope over a longer period; say, at
2-minute intervals over 8 minutes, rather than at 1-minute intervals over 4,
still completing the whole job within an hour? The snag, coming with that,
would be that the slope would be a fit to data that would be more curved,
less of a straight line. Anyway, having now seen the problems, lets agree in
advance about any changes which will make the best of the observations. It
promises to be instructive.

I note that Jim doesn't complain about my choice of +/- 1' rms of scatter,
to impose on the simulated sextant observations. It's that scatter that
upsets his analysis, more than anything else. It was partly on the basis of
his 1985 paper in "Navigation" that I chose that figure for sextant scatter.

Jim mentions that he expects the altitude curves to have a different slope,
rising and falling, but any deviation from symmetry will be so small as to
be quite imperceptible, at corresponding altitudes before and after the
observed peak. North-South speed shifts the parabola in time; otherwise, it
remains just the same parabolic shape, with no asymmetry about its shifted
peak. If he disagrees, it needs arguing out.

======================

Hewitt has applied his own method to three examples, and has confined those
to examples in which the answers have been provided in advance, although I
have urged instead that he should tackle a different data set, "blind" to
the answers. And he has arrived at three answers which are all remarkably
close, differerng from the original longitude by only -1.0', +4.5', +3.9',
respectively. It's hard to say much about the scatter from only 3 tests, but
it would appear that somehow he has tricks up his sleeve that are allowing
him to achieve much better results that Dave Walden's statistical analysis,
with its rms scatter of around 10'.

It would convince any doubters, if he would apply his skills to (some of)
the attached blind data set, noon2a.doc, which I attach once again.

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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```

File: 108059.noon2a.doc
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