Sect_7.2.7

7.2.7 Basic Modelling Concepts

THE STRUCTURE OF THE NORMAL EQUATIONS

Observation example:

R = 2 receivers, S = 4 satellites, E = 60 epochs

There are a total of 180 independent double-differences =
(R-1).(S-1).E.

Parameters:

6 coordinate components.
3 double-differenced ambiguity parameters, OR 4 single-differenced ambiguity parameters, OR 8 undifferenced ambiguity parameters.

Hence 6 parameters are to be estimated, 3 baseline components and 3 ambiguity parameters, because:

one station has to be held fixed, and
1 (single-differenced model), or 5 reference (undifferenced model) ambiguities have to be held fixed.

The Undifferenced Model

In the case of double-differenced observations, using the undifferenced ambiguity model, the structure of the Normal Equation system is illustrated in Figure 1 below, where:

Figure 1. The structure of the Normal Equation Matrix for the
undifferenced ambiguity model (2 receivers, 5 satellites).

Note that three (3) coordinate parameters and six (6) ambiguity parameters are not estimable!

The Double-Differenced Model

In the case of double-differenced observations, using the double-differenced ambiguity model, the structure of the Normal Equation system is illustrated in Figure 2 below.

Figure 2. The structure of the Normal Equation Matrix for the double-differenced
ambiguity model (2 receivers and 5 satellites).

Note that three (3) coordinate parameters are not estimable, although all ambiguity parameters are estimable!

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