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Using
"Weighted Stations" in GeoLab
GeoLab's versatility in
handling virtually any type of survey traverse or network adjustment is
due mainly to its capability of handling many types of
measurements - from GPS to conventional measurements such as
angles and distances, to leveling measurements. This versatility extends to the
capability of rigorously handling "weighted station"
adjustments.
A weighted station adjustment
is one in which the control stations are "weighted", which
really means that the control stations are free (not fixed),
and a set of coordinate observations are used to specify the
coordinates and covariance matrix for those control stations.
Normally the source of the "observed" coordinates and the
corresponding covariance matrix is a previous network
adjustment.
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For example, suppose we
are contracted by our friendly government agency to extend
a control network. In our example we will keep the number
of stations involved small - we will use three control
stations and three new stations as depicted in the figure
on the right.
The three points A, B,
and C are the three control stations, and the points 1, 2,
and 3 are the new stations.
The government agency
asks us to extend the A, B, C network with the three new
stations using GPS, and they provide us with the
coordinates and corresponding covariance matrix in the form of
"extracted observations" from a previous GeoLab
adjustment.
Please see the
weighted station IOB file to see the format of
these extracted observations. Note that we renamed this
IOB file (to a TXT file) so that your browser will know how to open it in
your default text editor. |
These coordinate observations were extracted from a larger
network adjustment using the "Network/List/Extract
Observations..." menu item in GeoLab. You can also see the GPS
measurements made for the extension in the
weighted station IOB file. Note that no stations are fixed
in this adjustment because the coordinate observations, or
"weighted stations", provide the required coordinate
information to the adjustment.
You can view the GeoLab
output listing for this adjustment by
clicking here. Note that we
have also renamed this file so your browser will open it for
you.
That's about all there is to
performing a "weighted station" adjustment. You can see in the
output listing that the control
station coordinate observations (as well as our GPS
measurements) receive residuals in the adjustment since they
are (correctly) treated as measurements by GeoLab. This allows a more
comprehensive analysis of the adjustment because you can also
analyze the quality of the control station coordinates by
analyzing the corresponding residuals.
Note that after we complete
the weighted station adjustment, the adjusted coordinates of
the control stations will be slightly different (adjusted) from the
values we started with. If the coordinates provided to us are
published coordinates that cannot be changed, the new adjusted
values would be not be published (unless our adjustment caused
large coordinate differences for one or more of the control
stations of course). Even though our weighted station
adjustment may not normally result in new published
coordinates for the control, we have propagated the
control network's covariance information into our network
extension.
A Neat Trick
The above point about
analyzing the control coordinates in a weighted station
adjustment can be used in "normal" integration/extension
adjustments. A typical adjustment situation requires that we
hold some existing control coordinates fixed when adjusting
our new survey measurements. The problem with doing that,
however, is if there is a "bad" control point (with inaccurate
coordinates, or the station marker was moved), it is usually
difficult to find the problem.
To illustrate how we can use
GeoLab's weighted station capability to better analyze the
control stations, two more IOB files were created. These are
both based on the weighted station IOB file above, and are as
follows:
To create the second one, we
started with the first one, and then selected GeoLab's
"Edit/Insert/Coordinate Obs" menu item. In the Coordinate
(Difference) Observation Group dialog that appears we did the
following:
- In "Obs Group Type" we
selected "3D Coords (3DC)"
- In "Matrix Type" we
selected "Generated"
- In "Matrix Coord System"
we selected "N, E, Up (LG)"
- In "Matrix Form" we
selected "Diagonal"
- In "Obs Type" we selected
"PLH"
- We un-checked all check
boxes on the right of the dialog
- We set the "Number of
Observation Records" to 1
- In "Matrix Additive
Values" we set all to zero except for "Diagonal" which we
set to
0.02
- In "Matrix Factor Values"
we set all values to 1
When you press the OK button,
the following records (lines) should be inserted into your IOB
file:
3DC
PLH 000 Station Name N 0 0 0.000000 E 0 0 0.000000 0.000 m 0
GENC LG DIAG 0 1 0.02 1 0 0.00000 1.00000
To arrive at the final
weighted station trick version of
our IOB file, we replace the generated PLH line in the above
to the unfixed control station PLH records. When we do our
adjustment using this version of the IOB file, the control
coordinates are now assigned residuals in the adjustment, so
if there is a bad control point, we will see it right away in
the residuals section of the
output listing.
This little trick was used by
a GeoLab user in Ontario, Canada, who discovered a control
point residual in the north direction of several centimeters.
When he examined the field book for the survey, he found a
note to the effect that this control station's monument
appeared as though it had be knocked north by a several
centimeters.
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