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    Re: Systematic error and its resolution
    From: Alexandre Eremenko
    Date: 2007 Apr 6, 12:24 -0400

    How do you determine the index error of a bubble
    I understand that some bubble sextants have two
    optical paths, one of them for the horizon observations.
    But if I understand correctly what sextant you are using,
    it does not have
    this option. So how do you determine its index error?
    In particular, I don't understand the sentence in your message
    "can be easily determined at the start of a round of sights".
    On Fri, 6 Apr 2007, Geoffrey Kolbe wrote:
    > In an otherwise correctly adjusted marine or
    > bubble sextant, the main source of systematic
    > error is Index Error, which can be easily
    > determined at the start of a round of sights.
    > Index Error in bubble sextants cannot be so
    > easily determined. So it is necessary to adopt
    > strategies to ensure that Index Error does not
    > does not affect the accuracy of the final position.
    > I spent some weeks in the Western Desert in Egypt
    > in March 2006 and had a lot of trouble getting
    > good fixes to start with. The problem was that
    > the desert is lot hotter than the Borders of
    > Scotland, where my A12 bubble sextant usually
    > resides, and so the Index Correction was no
    > longer the -7' that it had been for the past 20
    > years! Worse still, it seemed to change from day
    > to day. I finally came round to adopting a
    > strategy of taking sights on stars and the sun
    > when in the Cardinal points. The problems went
    > away and I started getting reliable fixes.
    > On my return, further research revealed that
    > Royal Air force navigators used exactly the same
    > strategy to ensure accurate fixes when using a
    > bubble sextant. Too, surveyors of old who had to
    > rely on a transit theodolite to determine their
    > position by stellar observations, also used the same strategy.
    > Last month I returned to the Western Desert,
    > again with an A12 bubble sextant - but not the
    > same instrument I had used last year. Back home
    > in Scotland, I had determined that an IC of +5'
    > had to be applied to this sextant to get the
    > correct altitudes. From previous experience, I
    > did not expect this to be a good IC in the Sahara
    > desert - and I was not disappointed!
    > Here is a round of sights
    > http://www.pisces-press.com/desert/14thMarch.jpg
    > I took when we reached Jebel Uweinat, the 6000 ft
    > mountain in the South West corner of the Western
    > desert. My estimated position was 21N55,25E10. I
    > did rounds of sights on the sun (morning and
    > evening), Polaris, Canopus and Regulus. I applied
    > the usual IC of +5' to the resulting altitudes.
    > Azimuths are in blue, position lines are green,
    > the red dot is where the GPS said I was when I
    > consulted it after I had obtained a fix by traditional means.
    > As can be seen, the box formed by the resulting
    > position lines is rather large, about 10' on a
    > side. From this, I determined that my IC should
    > have been more like +10' as the sextant was
    > reading about 5' too low. The resulting fix is
    > not bad however, just a couple of minutes away from the GPS position.
    > A few days later and a bit further North, when
    > camping next to Wadi Sora, (the "Cave of
    > Swimmers" made famous in the movie, "The English
    > Patient"), I did another round of sights, this time applying +10' of IC.
    > As can be seen
    > http://www.pisces-press.com/desert/19thMarch.jpg
    > this is altogether more satisfactory. All the
    > sightings (averaged and reduced) produced
    > position line intercepts less than 1' from the
    > estimated position. The GPS position subsequently
    > revealed that my EP was only about one minute
    > away from my actual position. With this
    > instrument, this result is really the best that
    > could be hoped for. But it should be noted that
    > the accuracy of my final fix is not actually much
    > better than it was when my IC was an unknown quantity.
    > In conclusion, I was able to get reliable fixes
    > far more quickly by moving away from the
    > traditional fix using three objects about 120�
    > apart with its resultant cocked hat, and adopting
    > a strategy of taking sightings on four objects,
    > each near one of the Cardinal points. I know that
    > if the box formed by the position lines is
    > substantially square, the errors are far more
    > likely to be dominated by systematic rather than
    > random errors. With a tradition
    > three-position-fix you never know if random or
    > systematic errors are dominating, so you can
    > never be sure just how accurate your fix is.
    > Geoffrey Kolbe
    > >
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