Weighted Stations
The term "weighted stations" refers to a set of coordinates, of one or more stations, having an associated weight, covariance, or correlation matrix.
In other words, a set of weighted stations is a set of stations that has a GeoLab coordinate observation group associated with it - the coordinate observation group can be either a 2DC or 3DC group. For more 2DC and 3DC coordinate observation group details, see Using Observation Groups.
GeoLab's versatility in handling virtually any type of survey traverse and 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.
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.
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 Stations IOB File to see the format of these extracted observations (you can save the contents of that page as an IOB file that you can adjust in GeoLab).
These coordinate observations were extracted from a larger network adjustment using the "Extract Obs..." button in GeoLab's Project/Tools tab. You can also see the GPS measurements made for the extension in the Weighted Stations 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.
If you wish to view the GeoLab output listing for this adjustment, just save the IOB file as mentioned above, and run the adjustment.
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 the 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 normally be published (unless our adjustment caused significant 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:
The Fixed Stations IOB with all control points fixed, and
The Weighted Station Trick IOB version.
To create the second one, we started with the first one, and then selected GeoLab's "Insert... Coord/diff obs" right-click menu item in the Assistant's text editor. 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 (which you can see by doing the adjustment).
This little trick was used by a GeoLab user in Canada to discover 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 several centimeters.