Sect_9.4.5

9.4.5 Modifying the Stochastic Model

MULTI-BASELINE VCV MATRICES FROM SINGLE BASELINE REDUCTIONS

Trivial Baselines in a Network Adjustment?

In the example referred to earlier, "quasi-independent" baselines from sessions A, B, C and F were included within the adjustment. There are a total of 32 baselines, of which only 20 can be classed as independent. If only the 20 independent baselines were included in the multi-session adjustment, and the iterative process of modifying the observation VCVs described above was used, it was found that the appropriate value of b that leads to a satisfactory variance factor is 5ppm for all baselines (the value of a was unchanged). The most noticeable effect is now in the size of the resulting error ellipses, some are up to 50% larger (see Figure below).

The main argument against incorporation of all baselines (independent and trivial) into a network adjustment is that the resulting solution statistics are "over-optimistic", that is the length of the axes of the error ellipses (or ellipsoids) are smaller than when only the independent baselines are used. Although there is at present by no means a total consensus on whether to include, or not to include, trivial baselines in any adjustment, there is strong support for including so-called "quasi-independent" baselines in network adjustment, for the following reasons:

It can be argued that all baselines reduced separately (and particularly if an ambiguity-fixed solution is obtained) are in fact independent.
Including all baselines from a session, if reduced separately, would (partly) account for the between baseline correlations that have been ignored at the single baseline reduction step.
Increasing the number of observations, and hence the redundancies (or degrees of freedom), permits more reliable statistical testing.
The use of all baselines, independent and quasi-independent, removes some of the arbitrariness involved in the selection of only independent baselines (different sets of independent baselines may lead to differing results). The outcome is a unique solution.

Example of relative 2-D error ellipses from a network adjustment involving
only independent baselines (compare with Figure in section 9.1.3).

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