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Hi Jim

I offer that the observer could simply just take data points every 5 minutes 
and let the computer fit the curve.  Dave Walden did just that and the curve 
fit eliminates the requirement that we be centered around LAN  or that the 
data be in some particular format.  Dave used a least squares fit, one form 
of regression analysis.  There are other forms of regression analysis, least 
squares is just one.

When we perform curve fits, iterative analysis or any other mathematics which 
would require a computer, simply due to the great quantity of computation, we 
make the navigational method more black box.  Witness Jeremy's use of the 25 
observations in the rapid fire fix method we have been discussing.  Jeremy, 
through no fault of his own, is limited to what is exposed to the user (him). 
 Without a lot of digging, the internals are hidden.  That's a black box. In 
this case, your form of regression analysis is hidden to you.  It may be a 
least squares fit, it may be something else. That's black box.

The most extreme example of this is the GPS.  We look at it and it tells us 
our position.  That's black box.

Re-examine that in light of the method you offer.  The method offers up a 
determination of the latitude and longitude from a noon (rapid fire) series 
of sights. If your method requires a computer and complicated regression 
analysis, why not just use the GPS?  Clearly, based upon comments from 
others, this type of fix predates computers, so it should be possible to 
manually determine.  The improvement you offer has to do with the structuring 
of the data and fairing straight lines, an easy day compared to a curve fit.

I don't expect that the method will provide the same statistical level of 
accuracy of a least squares curve fit.  It's nonsense to believe otherwise, 
as each observer put his personal spin on the line fairing.  We expect them 
to be "in the ballpark" and "about right", not perfect.  Give your method a 
fair twirl!

Best Regards
Brad





-----Original Message-----
From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of James N Wilson
Sent: Wednesday, April 29, 2009 11:56 AM
To: NavList@fer3.com
Subject: [NavList 8101] Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT


Brad:

I'm sure that least squares is better, but I used regression analysis
because that was what I had. I'm a complete novice at this mathematical
curve fitting. I was grasping at straws to avoid asking for more data
points. I've looked at a good many student sight plots, and they are
almost uniformly on a straight line. But they are taken with a sharp
horizon. I suspect that a hazy horizon would yield the kind of data that
George generated.

Being curious, I immediately tried this new toy on my ancient data
example. It placed the ascending line in exactly the same place that I
had eyeballed it, and had only a slight difference in the descending
line. The net result was a slight improvement in accuracy. In eyeballing
sights, I tend to throw out ones quite a ways from the trend, whereas any
curve fitting algorithm will use them all.

In looking at the final results, sights taken in runs centered around LAN
would be more utile than ones taken around highest altitude. That would
eliminate the extrapolation. But, as George points out, the observer
doesn't know when LAN is yet. More sights could be taken, so that the
latter ones would avoid extending the data lines outside of the range
measured.

I think that I still have a lot to learn.

Jim Wilson
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