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    Fwd: Systematic error and its resolution
    From: Peter Fogg
    Date: 2007 Apr 6, 22:11 +1000

    Systematic error may come from two sources:

    1. A systematic error in timing, leading altitudes to be matched with a moment  that is consistently too early or too late.

    This will affect most those position lines that trend towards north/south, and least those running east/west, as a systematic error in timing will affect most those observations made towards the vicinity of a body's prime vertical (sights to the east or west) and least those towards the vicinity of a body's meridian passage.

    If separate observations are made for latitude and longitude, latitude will be unaffected by a systematic error in timing, while the calculated local line of longitude will be displaced by the extent of the error, which cannot be ascertained or corrected unless other quite independent methods of resolution can be used.

    2. A systematic error in altitude, such as using corrections with the wrong sign, damage to the sextant, anomalous refraction, and the like.

    Correction for systematic error

    If the error is systematic, each position line will be displaced equally by the amount and in the direction of the error.

    [Direction refers to whether the displacement is consistently towards or away from the direction of the observation; thus all towards or away from the sub-stellar point (SSP).]

    With the most simple fix, obtained from two intersecting position lines, it follows that the systematic error can be plotted. The fix must be displaced by the consistent error along a line that bisects the angle formed by the intersecting position lines. As this line (here dotted) passes through the intersection of the position lines it changes from plotting an unknown extent of systematic error towards the SSPs to plotting an unknown extent of systematic error away from the SSPs.

    [ If this is not clear it can be made so, and the proposition proved, by plotting lines that represent different amounts of systematic error: each set the same distance from and parallel to the two position lines, both towards and away from the SSPs. The intersection of all the parallel lines will form points along the dotted line.]

    With only two LOPs the extent of error must remain indeterminate, and its resolution not possible.

    This changes once there are three or more position lines. Each pair of intersecting position lines can be given its own bisecting dotted line representing the systematic error affecting those two LOPs.

    The dotted lines represent all the points at which an unknown extent of systematic error could be plotted for each pair of position lines. When these dotted lines meet at a point this ambiguity is resolved: systematic error has been quantified and eliminated. This point becomes the improved fix, one without systematic error.

    With systematic error and azimuths that cover a spread of less than 180 degrees the improved fix will ALWAYS lie outside the triangle, and away from the direction of observation.

    With systematic error and azimuths that cover a spread of more than 180 degrees the improved fix will ALWAYS lie within the triangle.

    And not just anywhere within it; as illustrated the fix, free of systematic error, will lie at the centre. There is no other place for it to be.




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