9.1.4 Introduction to GPS Network Processing

VARIANCE FACTOR TEST

The most common test involves the variance factor ( also known as the estimated variance of unit weight ) , where n is the number of observations, and u is the number of parameters. This test generally involves comparing the computed (or aposteriori) variance factor against a test statistic from the chi squared distribution, and is usually performed at the 95% confidence level HARVEY (1994):

(9.1-12)

If the observation residuals are consistent with their accuracy estimates (VCV matrices), and the residuals are normally distributed, then the estimated variance factor would be expected to take a value between about 0.6 and 1.6, depending on the degrees of freedom (n - u) in the adjustment (see Figure below).

If the test fails for GPS session adjustments it may indicate the presence of one or more of the following problems:

• Poor estimate of standard deviations and correlations of observations. The observation residuals are significantly larger or smaller than those implied by the apriori standard deviations. The apriori covariance matrix Q_{l l} is inappropriate and may require re-scaling.
  
• Model or systematic error. Are enough parameters held fixed?
  
• Significant gross errors in one or more of the observations, for example, blunders in the measurement of antenna height propagating into an incorrect baseline solution.
  
• Poor quality (low precision) observations.
  
• The calculations are incorrect, for example, there is a "bug" in the program.
  
• Typing error in input (observations, approximate parameters, or option switches). Have all the observations been included?

Note: It is possible to make an error of the type listed above and the solution residuals may still pass the variance factor test!

Variance factor limits. HARVEY (1994)

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© Chris Rizos, SNAP-UNSW, 1999