Backsights and default accuracy estimates

[M.J. Green]

Hi,
Thinking about it, the way a surveying program should ideally run, is to
consider the probabiliity distribution for each measurement taken, and do
calculations based on this.  Accurately calulating the probablity
distribution and doing calulations based on these is very hard and time
consuming.  Therefore, as the real probability distributions are unknown
and are too hard to manipulate, they are at some point approximated to
gaussian.
This leaves the problem of choosing what sigma (1 sd) is for the gaussian.
I believe the correct way to do this is to make a suitable approximation
for the probability distribution is, then calculate the standard deviation
of that.  This way the probability distributions have the meaning that
they were intended, rather than putting in a scale factor when choosing
how large one sd is, then putting the inverse if it in when deciding when
to complain.
For BCRA grade 5, I suggest this means that the surveyor was trying to
read to the nearest degree.  If he could do this perfectly, thenthis would
mean a top hat function between -0.5 and 0.5 degrees.  However there is
also instrument calibration, and the pointing in slightly the wrong way,
and reading error when the reading is about half way.  Due to this and in
the spirit of the abssolute bounds suggested by the BCRA, I suggest that
the a reasonable probability distibution would be linear in the region
between 1 and 0.5 degrees, and then flat between 0.5 and 0 degrees.  This
is of course just a guess but it should give a better guess as to the
magnitude of 1sd than either my previous top hat functions, or assuming
reading are gaussian and putting a percentage cut of that is within 1
degree.  This gives 1sd equals 0.456 degrees, or 1 degree = 2.2 sds.
When an error is thrown the probability of getting the readings that far
out or worse given everything was measured correctly can be approximately
shown.  This approximation becoming better the larger the loop closure.  I
believe that Olly may have already implimented this last bit.
Thanks
Martin