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    Systematic error and its resolution
    From: Geoffrey Kolbe
    Date: 2007 Apr 06, 17:12 +0100

    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 
    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 
    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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