Sect_9.3.6

9.3.6 Multi-Session Network Processing

WHAT TO DO ABOUT THE VARIANCE FACTOR?

GPS reduction software invariably produce VCV matrices that imply very high precisions of the estimated parameters. The input of the resulting parameters, and their associated VCV matrices, into a secondary network adjustment will produce a network VCV and variance factor that may also not be realistic. The statistical testing of the multi-session variance factor will therefore, in general, fail. The variance factor test is usually performed at the 95% confidence level, requiring the estimated variance factor to be generally between 0.6 and 1.6 (depending on the degrees of freedom of the adjustment -- Figure in section 9.1.4).

If it is assumed that poor quality baseline observations, and blunders, have been eliminated by careful screening and quality control, that the mathematical model is correct, and there are no typing errors in the network adjustment input file, there are several possible reasons why the variance factor test may fail, two of interest to us are:

Poor estimate of standard deviations and correlations of the observations.
The presence of model or systematic errors.

In the case of primary GPS phase data solutions it is generally the latter (that is, the neglect of unmodelled systematic biases, principally errors in atmospheric refraction or the orbit -- section 6.2.1) that are the problem. By neglecting to account for them, the resulting VCV of parameters will reflect only the phase observation "noise" -- which is only of the order of several millimetres, and the baseline-satellite geometry.

In the case of secondary adjustment of the output of GPS phase reduction software, the "observations" are the baselines, and their associated VCVs. Hence if the variance factor test fails it is generally because the VCV of the observations is unrealistic (for the reasons given above). It is possible to have systematic errors (for example, there may be a systematic shortening of all single frequency baselines), but in a minimally constrained adjustment such systematic errors are only likely to be important if different receiver types (or more particularly, their corresponding primary solutions) and different field techniques (conventional static, compared with "rapid static" or "stop & go" procedures) are mixed together.

What are the options in respect of GPS network adjustments?

In conventional network adjustments it is common practice to use the aposteriori variance factor (VF) to scale the estimated VCV matrix of the parameters (by the VF). Is this desirable for GPS multi-session solutions? Only if the network is "homogeneous", that is, if all GPS results are produced by the same software, processing data collected by the same receivers under similar field conditions (session duration, comparable interstation distances, etc.), and the network has a significant number of redundancies (number of observations >> number of estimated parameters). The correlations are preserved, only the precisions are changed.
Do nothing. An option to be exercised, for example, if the VF test passes, or if there is insufficient redundancy in the network. This would be the case, for example, if the VF test is carried out at a single session network level (section 9.2.1).
Derive the VCV matrix from covariance analysis of the phase reduction process. Phase simulation software can be used to propagate realistic systematic biases (such as orbit error, refraction uncertainties, etc.) into the VCV of the estimated parameters. However, this is not a viable option for GPS surveying because of the specialised software that is required.
Modify the observation VCV information. The solution can be iterated, changing the VCVs, until the VF test passes. The manner in which this can be carried out, and the rationale behind such a process, is discussed further in section 9.4.

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