Sect_9.2.3

9.2.3 Single-Session Network Processing

SELECTING THE BASELINES

There are a number of strategies for determining which (R-1)(S-1) combinations of two satellites and two receivers will be selected to form a double-difference observable. The most common are:

BETWEEN-SATELLITE differencing using the base satellite or sequential satellite differencing mode. This results in (S-1) independent double-differences per baseline (section 7.2.4).

BETWEEN-RECEIVER differencing using the base receiver or sequential receiver differencing mode. This results in (R-1) independent baselines (Figure 1).

For example, any of the between-satellite and between-receiver differencing strategies for R=3 and S=5 will lead to 8 double-difference observations per epoch.

Although the between-satellite differencing strategy can be easily automated, between-receiver differencing can be more complex, sometimes requiring analyst input. For example, the options available for selecting independent baselines from which to form double-differences in software may be:

User selected reference (or base) receiver.
User selected baselines.
Automatic selection of base receiver, such that the sum of all baseline lengths radiating from this station is a minimum.
Automatic selection of baselines, such that only the shortest (R-1) baselines are used.

The selection of the shortest baselines is a deliberate one, made with a view to maximising the chances of resolving (all or some of) the ambiguities subsequent to obtaining the ambiguity-free solution.

Figure 1. Options for selecting independent baselines.

Ambiguity Resolution

Ambiguity resolution in a session adjustment requires particular attention. As the double-differenced observations are stochastically correlated and the baseline parameters are functionally correlated, the estimated ambiguity parameters are therefore also correlated. Only in a MULTI-BASELINE adjustment is it possible to resolve ambiguities across baselines by making use of these correlations, through a process of "boot-strapping" from one baseline to another. For example, if ambiguities on a short baseline are resolved, then the subsequent (partially ambiguity-free, partially ambiguity-fixed) solution for the ambiguity parameters on the longer baselines (those not yet resolved) may allow these remaining ambiguities also to be resolved. Therefore, although the selection of baselines (for forming correlated double-differences) is arbitrary, as the same Normal Equation system will result, different v' vectors can be obtained, and hence a different RHS to the Normal Equation matrix.

Hence, for multi-baseline ambiguity resolution it is good practice to select the independent baselines so that they are the shortest possible. This could be through the use of the base receiver or sequential receiver differencing strategy (or some combination of these). Examples of "good" and "bad" baseline selection are illustrated in Figure 2.

Figure 2. Baseline selection for multi-station ambiguity resolution.

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