Variance Factor Settings: What are they, and why do we need them?

GeoLab, like most powerful software packages, has many features and options that we either never take advantage of, or do not know about. Instead, we frequently use the default settings. While default settings, for the most part, work well, we thought it might be a nice idea to introduce you to the various options and software settings in GeoLab so that you can be sure you're getting the most GeoLab has to offer.

This group of variables specifies how the variance factor is used in performing adjustments with GeoLab. Please refer to Geodesy The Concepts, by Vanicek & Krakiwsky (1982), Chapter 13, for further details on the significance of these selections.

There are three options you can set in the VARF record (or in Tools/Edit Default Options/Statistics tab/Variance Factor group):

• Known (or not known);
• Scale Covariance Matrix (or don't scale);
• Scale Residual Variances (or don't scale).

1. Known

If this box is checked (this option should always be set to YES) GeoLab will perform adjustment statistics assuming the variance factor is known. If it is not checked, the statistics will be performed assuming the variance factor is unknown.

This option specifies whether the variance factor should be considered known or unknown. The main consequence of this setting is the probability distribution used for performing statistics on the estimated variance factor and for scaling the covariance matrix of the parameters. When known, the Chi-Square distribution is used, and when not known, the F distribution is used.

This option should always be set to YES (known) because, once the minimum constraint adjustment is done, you have estimated (as reliably as possible with the measurements you have) the variance factor, and you now know as much as you can about the scale of the covariance matrices of the measurements.

2. Scale Covariance Matrix

If this box is checked, GeoLab will multiply the parameter covariance matrix by the estimated variance factor. If it is not checked, this scaling will not be done.

This option should also always be set to YES (do the scaling). If the estimated variance factor is not 1.0, the covariance matrix of the parameters (if not scaled by the variance factor) would not reflect the actual accuracy of the measurements. When the estimated variance factor is 1.0, the scaling will not change the covariance matrix of the parameters but that's okay because the covariance matrix of the measurements is now properly scaled.

3. Scale Residual Variances

If this box is checked, GeoLab will multiply the residual variances by the estimated variance factor. If it is not checked, this scaling will not be done.

This option should also always be set to true.

When you have performed your final adjustment, the estimated variance factor should be 1.0 and this scaling will have no effect. However, when doing preliminary adjustments, the variance factor will not normally be 1.0 and when the standard deviations of the residuals are calculated, unrealistic values will result if the corresponding variances (of the residuals) are not scaled by the variance factor (making it very difficult to analyze the residuals). When this option is YES, the resulting standardized residuals (residual divided by its standard deviation) will be realistic, and their values won't be unduly affected by an improper scaling of the measurement covariance matrices. In other words, when this option is YES, you get a clear picture of the standardized residuals even if you haven't yet scaled the measurement covariance matrices properly.