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    Systematic error and its resolution
    From: Geoffrey Kolbe
    Date: 2007 Apr 07, 08:08 +0100
    Frank said (posting #2539):
     "I think the approach would be to vary the fixed correction until the box surrounding the crossing points of the various LOPs is as small as possible. "

    I would agree Frank, with the proviso that all the LOPs should either be "away from" or "towards"  the celestial objects concerned. The little arrows we put on the LOPs to signify the direction of the celestial body should all point out of the box or into the box. This is essentially the same as determining your IC for that particular round of sights.

    Frank also said:
    "This should work even in cases at arbitrary azimuths and with random errors, too."

    Thank you Frank, I was hoping somebody would say that.....

    Generally, if your estimated or assumed position is a long way from your actual position, there will some error in the first fix you get from the crossing of the LOPs. In those circumstances, it is usual to reduce the sights again, using your first fix as a new estimated position. It is a rapidly converging iteration process. The reason there is an error in the first fix is that the angle of the azimuths, and so the LOPs, will change depending on your estimated position. In general, the error in the first fix will go as the angular distance between estimated and actual position.

    However.... I have not analyzed it deeply, but I think that taking sightings at the Cardinal points is actually a special case. The reason is that our latitude-longitude coordinate system is a grid of North-South, East-West alignment.

    Take for example sightings taken on objects to the North or South, which essentially give latitude. If there is a difference between the estimated position from which the sightings are taken and the actual position, the error in the resulting latitude will go (to first order) only as the difference in longitude between the estimated and actual position. The difference in latitude will have essentially zero impact on the outcome. The same is true for sightings on objects to the East or West, which essentially give longitude. The error in the resulting longitude goes (to first order) only as the difference in latitude between the estimated and actual position. This means that finding your position by taking a round of sights on four objects, each of which is near a Cardinal point,  is relatively tolerant of errors in the estimated position.


    Geoffrey Kolbe



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