Fw: Backsights and default accuracy estimates

[Martin Green]

Hi,
The probability distributions that I suggested were not supposed to be
accurate.  I agree that a gaussian is a good approximation due to the
central limit theorem, but how wide a gaussian?  I think that guessing the
probability distibutions and calculating the standard deviation is better
than using a gut feeling to guess the number of standard devitaions.  This
is particularly as I suspect that the tails of the distribution will be the
least best approximation to gaussian, and in guessing width by what is
considered unlikely for a single measurement would fall foul to this.  Thus
giving a bias when considering the statistics of loop closurers where the
error will be a good approximation to gaussian.

Minimum value for grade 5:
1 deg = 1.73sds for a uniform dist. between -1 and 1
Correct order of mgnitude guesses:
1 deg = 2.2sds for a uniform dist. between -0.5 and 0.5 tailling of linear
to +/-1
1 deg = 2.45sds for a linear dist. between 0 and 1, and 0 and -1
Maximum value for digitization error of reading to 1 degree:
1 deg = 3.46 sds for a uniform distribution between -0.5 and 0.5

>From this table a suitable number between 1.73 and 3.46 should be choosen.
2.1 - 2.8 being probably the best range to choose within.

For individual people doing lots of calibrations over a large surveying
project.  Individual statistics for people and instruments may be possible
and more applicable.
Martin