"STANDARDISATION" OF VCV MATRICES TO ACCOUNT FOR BETWEEN-EPOCH PHYSICAL CORRELATIONS |
In section 7.2.5 it was mentioned that in fact strong between-epoch physical correlations have been noticed in GPS observations. The higher the data rate, the stronger the correlation (eqn (7.2-14)). These correlations should be included in the input VCV matrix of the phase observations used in the Least Squares adjustment of double-differenced phase observations in a baseline reduction. However, no commercial software takes this correlation into account, hence the output VCV matrix of the baseline component and ambiguity parameters is incorrect. The effect on the VCV matrix can be accounted for by a scale factor.
The fact that neglecting between-epoch correlations simply leads to an incorrectly scaled VCV matrix means that there has been no need to hitherto tackle this problem. During secondary network adjustment, failure of the Variance Factor Test is usually addressed by scaling the VCV matrix factor and repeating the solution. In this way, the scale factor (the aposteriori variance factor) is empirically determined, and accounts for a number of effects including the neglected between-epoch physical correlation.
There would therefore have been no need to explicitly consider the between-epoch correlation except for changes in the way GPS surveys are carried out has made the issue more than of passing academic interest. The scale factor is a function of the length of the observation session and the data rate. In conventional GPS surveying the observation session lengths are relatively long (30-90 minutes), and the ratio of the longest observation session to the shortest session is generally only 2-3. Hence the variances of the estimated baseline components are reasonably compatible and the secondary network adjustment can accommodate these baselines.
However, in the case of GPS "rapid static" and "stop & go" surveying (section 5.5.1), the observation times are comparatively short (from less than 1 minute to 15 or so minutes), and hence the ratio of the longest observation session to the shortest session can be very large. As a result, the variance-covariance matrices for different baselines, determined using a variety of observation session lengths, will have very large differences in the magnitude of the VCV matrix elements, which will cause problems during network adjustment.
HAN & RIZOS (1995b)
describes a procedure by which the baseline co-factor matrix may be scaled
by an appropriate factor 
that accounts for the neglected between-epoch correlations
in the baseline reduction using phase observations:
 |
(9.4-8) |
where 
(
) is the correlation coefficient for data collected at
intervals of seconds, and n is the number of observations in the
session.
The standardised cofactor matrix is converted to the standardised VCV matrix through multiplication by the standardised variance factor (a formula for which can be found in HAN & RIZOS, 1995b).
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© Chris Rizos, SNAP-UNSW, 1999