Download The standard error of the mean for pointings would be

Star*Net
Instrument Settings
Options > Project… > Instrument tab
Star*Net Instructions
The values requested in this screen are the standard errors of the mean, which are derived from the standard
deviations of measurements types with the instrument, along with the method used (e.g. how many times an
angle is turned, then averaged). The standard deviations can be determined either by a controlled test, making
many repetitions of angles and distances, or by consulting the manufacturer’s specifications. The latter method
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is the one used by most surveyors. The following is copied from the Star*Net instructions (bold, italics and
underlines added):
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 dependent 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.
Specifications from Leica TPS1100 User Manual, pages 143 & 146
EDM Standard measurement to prism, “Accuracy”:
2 mm + 2 ppm (0.0065 ft + 2 ppm)
Angle measurement, “Accuracy”:
2"
Laser plummet, “Accuracy” Deviation from plumbline
1.5 mm (0.005 ft) (2 sigma) at 1.5 m instrument height
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Interpretation of the Leica specifications
I asked Jorden Friesen, at Microsurvey, how he would interpret the 2" listed as the accuracy of the
instrument. He thinks it is the “Direction” or “pointing” precision of the TCRA 1102. He suggested I ask
Leica.
I asked Darrell Groda, a good Leica technician at Kuker Ranken and he didn’t know any more than me
about this. He recommended that I contact Leica Technical Support through Kuker Ranken phone
service (425-412-7100). I did this, and the man that I talked to believes that the stated accuracy of 2"
for the Leica TCRA 1102 is referring to angle accuracy rather than pointing accuracy. He consulted with
another Leica technician and he agreed.
On November 25, 2013 I received an email from James Johnston, Technical Support and Training
Manager for MicroSurvey, and he said in most cases the instrument settings are reported as “pointings,”
but if I wanted to assure myself of that fact, I should ask if the instrument specs are reported as per DIN
18723. Subsequently, I did a Google search for DIN 18723. One of the results was a newsletter
published in September 2002 (DIN18723_Leica.pdf) by Leica about DIN 18723. It used some
mathematical terminology unfamiliar to me, but it seemed to indicate that Leica’s precision
specifications are per the DIN 18723, and do refer to “pointings.” I also found an informational paper
published by Leica, dated May 1999, about the “new generation” of total stations from Leica, the
TPS1100 Professional Series. This document clearly states that the angle-measuring accuracy is “in
accordance with DIN 18723.” It also specifies that the angle-measuring accuracy of the TPS 1102 (my
instrument) is 2" in accordance with the DIN 18723 standard.
Conclusion
My Leica TCRA 1102 instrument is rated for angle-measuring accuracy “in accordance with DIN 18723” at 2"
which means the standard deviation (σ) for directions (pointings) is 2". This means that there is a 68.3%
chance that any single directional reading will be within 2" of the mean of a series of measurements.
An angle measurement is composed of 2 directional readings (pointings). The formula for the standard
deviation (σ) for angles is:
𝜎𝑎 = 𝜎𝑝 × √𝑛
where 𝜎𝑎
𝜎𝑝
n
= Standard deviation of an angle measured
= Standard deviation of a direction (pointing)
= Number of pointings
If the standard deviation (σ) for pointings is 2", then the standard deviation (σ) for angles is
𝟐" × √𝟐 = 𝟐. 𝟖𝟐𝟖"
This means that there is a 68.3% chance that any single angle measurement (BS direct - FS direct) will be within
2.828" of the mean of a series of measurements of that angle.
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Star*Net Project Options, Instrument default settings requires the standard error of the mean (𝝈𝒎 ) for various
measurements made with the instrument. The formula for the standard error of the mean (𝜎𝑚 ) is:
𝜎𝑚 = ±
𝜎
√𝑛
where 𝜎𝑚
σ
n
= Standard error of the mean of angles measured
= Standard deviation of angles measured
= Number of times an angle is measured
Angle
For my control work, I turn 2 sets of angles, which is 4 angles (BS direct, FS direct, FS reverse, BS reverse, BS
direct, FS direct, FS reverse, BS reverse). My onboard TDS software averages the 4 angles and records the
average in the .rw5 file. So the standard error of the mean for my angles (the default values entered in the
Star*Net instrument options) would be:
𝝈𝒎 = ±
𝟐.𝟖𝟐𝟖"
√𝟒
= 𝟏. 𝟒𝟏𝟒"
This means that the mean of the 4 measurements of an angle has a 68.3% probability of being within 1.414" of
the true value of that angle.
Direction
If I am using direction (pointings), such as would be done with a directional theodolite, I would likely make 4
pointings to each target. The standard deviation (σ) for directions (pointings) is 2" per the DIN 18723 specs.
The standard error of the mean for pointings would be:
𝜎𝑚 = ±
𝜎
√𝑛
𝝈𝒎 = ±
𝟐"
√𝟒
= 𝟏"
This means that the mean value of the 4 pointings at a target has a 68.3% probability of being within 1" of the
true value of that pointing.
Distance Constant
For my control work, My TDS software measures the distance once, so I would use the 2 mm (0.0065 ft)
specified by Leica.
Distance PPM
For my control work, My TDS software measures the distance once, so I would use the 2 ppm.
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Aliases
Use the inline .ALIAS NAME option to define points that are re-observed using a different point number (which is
required with TDS). Aliases must be defined before they appear in the data files.
This is the point
to be aliased
These are aliases
for point 1
.ALIAS NAME 1 4 5 6
.ALIAS NAME 2 7
C 1 1000.0 1000.0
BM 1-2 0 100.0
…
M 12-11-4 123.45 90.0130
M 12-11-7 134.23 90.1234
…
M 15-14-5 543.21 89.5830
EXAMPLE
#Points 4, 5 and 6 are explicitly aliased to point 1 (4, 5 and 6 are now
alternate names for point 1)
#Point 7 is explicitly aliased to point 2 (7 is now another name for point 2)
#Point 1 is defined here
#Point 2 is defined by azimuth and distance here
#Re-observation of 1 was stored as 4
#Re-observation of 2 was stored as 7
#Another re-observation of 1 was stored as 5
The inline .ALIAS PREFIX and .ALIAS SUFFIX options cannot be used with the data from my TDS program because
TDS will not allow me to name points with alpha characters. I can only use numbers.
Grid Coordinate System (Using Washington State Coordinate System - NAD83)
To use points in the Washington State Coordinate System (NAD83), in the Project Options, Adjustment tab,
select Grid for the coordinate System. Select the horizontal datum (NAD83)and the Zone (4601 WA North).
For the Average Geoid Height, use one of the following web sites:
http://www.unavco.org/community_science/science-support/geoid/
http://www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/geoid03_prompt1.prl
http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/intpt.html
Enter the latitude and longitude of one of your points in one of the calculators on the web sites listed above.
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