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    Re: fix from repeated observation: was Re: Coriolis vs Noon curve correction
    From: George Huxtable
    Date: 2009 Apr 26, 21:02 +0100

    I've renamed this thread to be more appropriate.
    
    Jeremy wrote-
    
    "I am scheduled to take a very LONG ocean passage this next tour on my
    ship, so I intend to do quite a bit of Celnav during it.  I will try
    to "publish" a Nav journal on here when I am through.  I intend to try
    this method over a wide range of latitudes and Northerly declinations,
    as well as common sights and other exotica (expect numerous lunars as
    well)."
    
    That is something many navlist members will look forward to.
    
    He also wrote-
    
    "When I use the computer program on the ship for these sights (SkyMate
    Pro), I tell the computer the time I want the fix calculated for (I
    input either LAN or the nearest half hour), as well as the course and
    speed of the ship.  Assuming that the DR track is reasonably accurate,
    the lines are calculated, taking into account the varyed declination,
    and automatically advanced or retarded, taking into account ship's
    motion, to give me the 95% probablitly fix.  I then compare this with
    the exact GPS reading taken at that minute to see what kind of error I
    am getting.  With the sun and Venus, I consistantly got less than 1'
    of error in both Latitude and Longitude, and slightly more with the
    moon."
    
    I ask Jeremy to be a bit more specific about the observations that give him 
    "consistently less than 1' of error in both Latitude and Longitude". Are 
    these separate observations of two bodies to produce two crossed position 
    lines? Or are they observations of a single body repeated over a short 
    period, to provide a calculated fix, as in his posting about the Moon 
    recently referred to by Frank Reed as an example of what can be done.
    
    I had read that posting, [5416] of 6 June 08, which was a really good series 
    of Moon altiitudes, and have made a least-squares fit to it, which showed 
    that the random scatter in the observations was about +/- 0.3 arc-minutes 
    rms. That's pretty good going, even by big-ship standards, and I presume 
    that weather conditions were benign. If anyone wishes to refer back to it, 
    at http://www.fer3.com/arc/m2.aspx?i=105416 , they should be aware that the 
    times referred to as UTC were actually Zone time, and the UTs were all just 
    after 9h UT , as was pointed out by Guiseppe Menga.
    
    Jeremy wrote, later, about the result of that series of observations, in 
    [6066]-
    
    "Basically the given 1900 ZT position is a GPS fix, so that is what we can 
    assume to be the true position, and the celestial fix is an error check of 
    the GPS position (please no arguments on this point as it is beyond the 
    scope of this exercise.)
    
    I plugged each moonline into my celestial program (SkyMate Pro) as 
    individual moon LOP's.  The computer then compared them and gave me a fix of 
    14 deg 14.9' North; Longitude 142 deg 51.9' East at 1900.  This is a 1.7 nm 
    error as compared to the 1900 fix via GPS.
    
    The trouble with crossing an averaged LOP in this case with a course line is 
    that it does not give us a fix, but rather an "estimated position."
    
    This is an experiment I did to see if a fairly large number of sights of the 
    same body, shot in a relatively short period of time, could give us a 
    position of reasonable accuracy away from meridian transit.  As we can see, 
    it is fairly accurate, certainly accurate enough for a deep sea position. 
    The position probably would be more accurate if the change in azimuth of the 
    body was greater then 5.5 degrees, but that is why I shot the moon, as the 
    azimuth is changing rapidly, even away from the time or meridian transit."
    
    ================
    
    That experiment was certainly worth reporting. I had discounted it a bit, 
    presuming that in a one-off case, the close coincidence in both lat and long 
    was no more than fortuitous. But if Jeremy is really claiming that such a 
    short (8 minute) series of observations of a single body can CONSISTENTLY 
    give him such precision, perhaps it needs to be taken more seriously. Until 
    then, I retain my traditional scepticism.
    
    As Jeremy notes, he shoose the Moon for observations because its azimuth was 
    changing quickly, which can be the case for objects that are high in the 
    sky, as the Moon then was. If he is going to be in more Northern latitudes, 
    such high bodies may not be available.
    
    There's no doubt that Jeremy determined a very precise position line, at 
    right-angles to the direction of the Moon, which varied between 157.5� to 
    162� over the observation period. How (and how well) did his program 
    establish where he was along that line, and how precisely could it do so? 
    Did it provide an error ellipse, and if so, what sizes? Had it been provided 
    with a DR, and if so, was it perhaps using that DR to find its most likely 
    (closest) spot to the DR along that position line? If it had been provided 
    with a DR that was deliberately 10 miles further North (say), would it have 
    ended up with the same result? These are all questions that come to the 
    sceptic's mind. The more powerful a computer program gets, the less the user 
    tends to know about what's going on under the bonnet.
    
    So I welcome Jeremy's offer to make more such short series of observations 
    to find out whether those results are consistent. And request that some 
    tests are made in which the computer is given, not the GPS position, but 
    some deliberately displaced position, as DR, to see whether it comes up with 
    the same answers.
    
    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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