GeoLab's Adjustment Procedure

GeoLab performs least squares adjustments of survey networks. In such an adjustment, the inconsistencies of the observations are statistically removed by assigning residuals to them.

For example, if you measure the three angles of a plane triangle, their sum will not normally be 180 degrees because of small errors in the measurements. An adjustment will assign a residual to each angle so that they do add up to 180 degrees, and so that the sum of the squares of the residuals is a minimum (least squares).

In other words, the observations are adjusted (by assigning residuals) so that they are consistent with the geometry of the network.

This document describes the recommended approach to adjusting all types of surveying and geodetic networks with GeoLab.

The figure to the right illustrates the general steps, or processes, for performing GeoLab adjustments, with some of the details for each step given below the diagram. The steps contained in the “Repeat for each observation set…” rectangle, should be performed for every observation set that can be meaningfully adjusted by itself (e.g. the observation set must have a sufficient number of degrees of freedom and network connectivity for a reliable statistical analysis to be performed). This will ensure that we determine the best estimates for the observation covariance matrices.

Normally, an “observation set” in this context, means an independent set of measurements gathered by a different instrument, on a different day, etc – the differences between the observation sets are such that the covariance matrix for that set will be expected to be different from another set, even if the same set of instruments were used. Because this approach will allow us to arrive at a more reliable and statistically meaningful network adjustment, one should design the network measurement logistics so that independent sets of measurements can be meaningfully adjusted by themselves.

Note that, when we perform a least squares adjustment, we are determining the following:

  • The most probable (maximum likelihood) estimates for the values of the station coordinates and any auxiliary parameters.

  • The most probable estimates of the observation covariance matrices for all observations in the adjustment (when the estimated (a posteriori) variance factor is different from 1 (the a priori variance factor), and we have resolved any blunders or mistakes in the measurements, the estimated variance factor is nothing but a factor for the measurement covariance matrices to make them more realistic (this is precisely what we do when we calculate the mean (average, or most probable value) and variance from a sample of measurements (which is, of course, a least squares adjustment process itself)).


The adjustment steps are as follows:

  • Step 1: Prepare Measurements, Coordinates, & Geoid
    In this step, you get your measurements, initial coordinates, and geoid ready for use in the adjustment. For measurements, you may first have to import them (using GeoLab’s “File/Import…” menu command) into a GeoLab IOB file if they are still in another format (e.g. Leica SKI Pro, Trimble Data Exchange format, TDS format, etc). You also may have to pre-process your measurements, as you always have to do with GPS vectors, for example For initial coordinates, you may have to scale them off maps, or transcribe them off control coordinate sheets, etc. For the geoid, you may have to check that the GSP file is set up correctly to use the proper geoid data (undulation) file.

  • Step 2: Prepare the Main IOB File
    In this step, you organize your measurements into separate IOB files that can be #included in your main project IOB file. You can also create a separate IOB file that will contain any options that you wish to incorporate directly in your IOB files. You should also create another IOB file for your initial coordinates, which will be #included in your main project IOB file. Finally, a GFIL record should be added to your main project IOB file just after the #include for your initial coordinates. After this step, your main project IOB file will look something like the following:

    #include “Options.iob”
    #include “InitialCoords.iob”
    GFIL “c:\Geoids\MyGeoid.gsp”
    VSCA 1.0000
    #include “TraversObs.iob”
    VSCA 1.0000
    #include “Leveling.iob”
    VSCA 1.0000
    #include “GPSObs.iob”

    Note that each observation set is assigned a “VSCA” record, which will be set to the estimated variance factor after the separate minimal constraint adjustment and analysis of that observation set.

  • Step 3: Perform Minimal Constraint Adjustment
    In this step, you open your main project IOB file in GeoLab, and run the adjustment with the “Network\Process the Open IOB File…” menu command (or click the corresponding toolbar icon). Note that you can easily adjust each observation set separately by commenting-out the VSCA and #include records for all other observation sets. For example, you could start by doing a minimal constraint adjustment of only the “TraversObs.iob” measurements with the following setup in the main project IOB file:

    #include “Options.iob”
    #include “InitialCoords.iob”
    GFIL “c:\Geoids\MyGeoid.gsp”
    VSCA 1.0000
    #include “TraversObs.iob”
    *VSCA 1.0000
    *include “Leveling.iob”
    *VSCA 1.0000
    *include “GPSObs.iob”

    After the network processing (adjustment) is completed, the “Network Processing Completed” dialog will be displayed. At this stage you should just click the OK button, and then the “Adjustment Results Summary” dialog is displayed, which displays any large standardized residuals that you will have to analyze (the largest standardized residuals are displayed at the top of the list on the bottom-left of this dialog – you should double-click the largest of these standardized residuals to scroll the output LST file to the residual listing for the corresponding measurement.

  • Step 4: Analyze Residual Outliers
    The analysis of the residuals is done as follows:
    · For large standardized residuals, you should compare their absolute value to the “critical value” reported at the top of each residuals listing page in the adjustment output LST file. If the standardized residual is larger than the critical value, then you must determine if there is a problem with the corresponding measurement. For example, in the case of a GPS vector measurement, if a standardized residual has the value 6.7, and the critical value is 3.8, it is likely a bad measurement that has to be removed (commented-out) from the adjustment.
    · You should also always examine the residual itself, because even if the standardized residual is a bit larger than the critical value, the residual may be small enough, and the measurement can be left in the adjustment.
    Note that you should never remove more than one measurement from the adjustment at a time, and the measurement you remove should always be the one with the largest standardized residual.

  • Step 5: Edit Measurements
    Normally, when a large standardized residual results, you should first attempt to find the reason for it, and if one is found then the measurement should be corrected. If no reason can be found, the measurement can be re-observed, or it can be removed (commented-out) from the adjustment.
    In this step, you should also use the resulting preliminary adjusted coordinates as initial coordinates. To do so, you can use the “GeoLab Adjusted Coordinates Lister” (“Network/List/Adjusted Coordinates…” menu command) to produce a new list of coordinates, which you can copy and paste as new initial coordinates in your initial coordinates IOB file.

  • Step 6: Scale Observation Covariance Matrices
    After you have resolved any problems with the measurements, and there are no remaining standardized residuals larger than the critical value, you should use the estimated variance factor from the last adjustment you did for the observation set in the VSCA record for that set. This analysis and observation covariance matrix scaling procedure should be used for each observation set in your network. Once all observation sets are analyzed separately, you can then include all of them into your adjustment, each with its separate VSCA record, and perform a final minimal constraint adjustment (which will likely produce an estimated variance factor slightly different from 1.0).

  • Step 7: Perform Over-Constrained Adjustment
    If you have to perform an over-constrained adjustment, you will normally fix or weight more control stations than the minimum necessary. This is normally required to ensure that the new network fits well with all control points in the area.
    Of course, when you add more fixed or weighted control stations, the measurements in your network will be forced to fit all such constraints, and in general, residuals will increase in absolute value, and therefore the variance factor will also increase in size. You will simply have to re-scale all VSCA values with the new variance factor and re-run the adjustment.

More InformationMitch Palmerinformaiton, adjustments, help