Sect_12.1.3

12.1.3 Constraining GPS Networks

THE CONSTRAINED NETWORK SOLUTION

An alysing External Adjustment Results

As is the case with any Least Squares adjustment, there are a number of indicators that should be checked. Analysing adjustment output is a topic of its own. Although there may be a number of well documented procedures that may be followed, it must be emphasised that quality control analysis of adjustment results is as much an "art" as a "science". The challenge is to use the indicators available to (a) determine whether the adjustment was successful, but if not, to (b) interpret the telltale indicators as to the possible source of the error or distortion in the adjustment. The former should be routine, while the latter more correctly belongs to the set of "trouble-shooting" procedures.

Some of the indicators are statistical in nature, for example many analysts look immediately to the variance factor. But there are, in addition, the results of various statistical tests on the residuals and on the estimated parameters, the correlations between parameters, etc., to be noted. Some indicators are deterministic, for example, the "root-mean-square" of the residuals, the largest residual, etc. But there are a large number of indicators which cannot be so easily classified. They belong to a "fuzzy" group of indicators that generally are very application specific. For example, in Chapter 7 and Chapter 8, several "rules-of-thumb" for double-differenced phase solutions were quoted. In the case of secondary network adjustments (either minimally constrained or incorporating external control information), drafting such "rules-of-thumb" is more difficult. The following is merely a list of some ingredients of a "good adjustment":

The network must have "symmetry": well spaced stations within the network, well spaced control points and a "well shaped network" (for example, not linear in form).
"Sufficient" degrees of freedom in the adjustment.
Control station coordinates of approximately similar accuracy (for example, mixing spirit and trigonometrically levelled heights can lead to problems if the VCV information is not accurately defined).
The observations should be relatively homogeneous (mixing results from different eras, different field procedures, or from different software, may lead to problems).
Careful trouble-shooting should have been exercised at all earlier phases of the adjustment, by following the strategy of "adjust a little, test a little".

There are a number of further points that can be made with reference to the combined adjustment solution, although they are not elevated here to the status of "rules-of-thumb":

Any large residuals or corrections to the coordinates usually indicate a problem with the control information. Following the quality control tests made on the GPS-only solution, this solution can be assumed to be largely free of error. The cause of error may be incorrect control coordinates in the local datum.
If the large residuals are generally restricted to the vertical components, this may indicate a height error at the control stations. A common error is to input the available levelled (or orthometric) height, rather than the ellipsoidal height. Even approximate values of the geoid height, as obtained from a spherical harmonic model (section 11.3.5), can often appreciably improve an external adjustment.
The aposteriori variance factor should be examined. If it is greater than unity this indicates either that the uncertainties assigned to the control information are too low, or the GPS-only observation precisions are too optimistic. Either of the VCVs may be scaled to obtain a more "balanced" solution.
The resulting transformation parameters should not be large (>0.5ppm in scale, >0.5" in rotations, but beware of the strong correlations between rotations and translations) as this may indicate a possible problem with the control information. Large uncertainties in the parameter estimates may also be evidence for this. Some trouble-shooting may isolate the problem, but only if there is sufficient redundancy in the external adjustment (more than the minimum number of common points in the GPS and local network).
The statistical indicators should be studied first. If there is a hint of a problem, generally the next step is to scan the residuals. It may or may not be possible to immediately pinpoint the source of the problem. If it is not obvious (and it is not uncommon to have more than one error, the effect being for the errors to interact and to cloud the sources of the problems), certain trouble-shooting procedures such as investigating loop closures (section 10.4.3) may have to be resorted to.

Solution Output and Survey Classification Issues

As with the primary GPS reductions described in Chapter 7, and the secondary (GPS-only) network adjustments discussed in Chapter 9, "quality control" is an important issue (Chapter 10). There are a number of strategies that can be used to verify the quality of the adjustment, some specific to the external adjustment, others common to all types of Least Squares operations. One of the biggest differences is the scope for finally estimating the GPS accuracy, if the external ground coordinates are of the adequate quality. This also impinges directly on the issue of survey accuracy assurance, as discussed in section 10.2.2. As a reminder, there are two levels of GPS survey result accreditation in Australia and the U.S.:

Those that are a function only of the field survey methods, reduction techniques and the results of minimally constrained network adjustment -- the CLASS.
Those that are a function of the above AND the conformity of the new survey results with the existing network coordinate set after the transformation process required to convert results from the original datum (WGS84 in the case of GPS) to the local geodetic datum -- the ORDER.

If the external control is superior to that expected from the GPS survey procedures used (which in Australia define the CLASS of survey), then a distortion of the GPS-only net to fit the external control does not degrade the quality of the GPS results. The resulting GPS survey ORDER will not be greater than the CLASS.

However, if the surrounding control information is of a poorer quality than that expected from the GPS survey procedures used, then the external adjustment will lead to a GPS survey ORDER classification that is lower than the CLASS. That is, the GPS survey will be classified as having an ORDER no higher then the external control, no matter how precise (or how high the CLASS) of the survey.

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