STAR*NET V6 - Circe

Chapter 4 Options
What standard error settings should be used as project defaults?
Before you can determine what standard errors to use as project defaults, you must know
the standard deviations of measurement types based on the equipment used. These are
called the “population” standard deviations, meaning they are statistically derived from a
large number of measurements. There are two ways of determining these values:
1. Compute Them from Testing: You can set up a controlled field test and observe
many repetitions of angles and distances. The procedure is described in many text
books, however it is seldom used because of the time and effort required.
2. Use Manufacturer’s Specifications: This method is used by most surveyors. If your
equipment is in proper working order and you follow accepted procedures, you can
use the manufacturer’s population standard deviation estimates as a basis for
determining what standard errors to use as default settings for your project.
Note that most theodolite specifications are stated in terms of a “pointing” precision, the
ability to repeat a reading to a single point. An “angle” is made up of two pointings.
Therefore, if a given pointing specification is 5 seconds, you would propagate an angle
standard deviation by taking 5 seconds times SQRT (2) = 7.07 seconds.
As an example of population standard deviations for a total station, let’s use 7.0 seconds
for angles, 5.0 seconds for pointings, and 0.03 feet plus 4 ppm for distances. Using these
manufacturer’s population standard deviations, what standard error values should be
used as the project options instrument default settings?
First of all, the term “standard error” is short for “standard error of the mean.” It is an
estimate of the uncertainty of the mean (or average) of a set of field observations. The
equation for standard error of the mean is:
Std Error = Std Deviation / SQRT ( Number of Observations Averaged )
If you average 4 angles, use 7.0 / SQRT (4) = 3.5 seconds as the standard error setting
for angles. If you average 4 direction pointings, use 5.0 / SQRT (4) = 2.5 seconds as the
standard error setting for directions. And likewise, if you average 2 distances, divide the
0.03 feet and 4 ppm by SQRT (2) and use 0.021 feet and 2.8 ppm as the standard error
settings for distances.
It is important to note that the standard errors calculated above are dependent only on the
population standard deviations and the numbers of observations averaged. They are in no
way dependant on the values or spreads of the actual averaged observations!
If you do not average observations (i.e. you enter every repeated measurement), simply
use the manufacturer’s standard deviations as your default standard errors. For example,
if you repeat an angle 4 times and enter all 4 observations, each angle would be given the
standard error of 7.0 seconds. Although more lines of data are created by entering every
measurement, some users prefer doing this knowing that their observations are always
correctly weighted in the adjustment, independent of the number of repeats.
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