Bernese GPS Software Version 5.0 - Bernese GNSS Software

9. Combination of Solutions
x
x 1
t 1
t 2
x 1
Figure 9.3: Addition of the new coordinate parameter.
station velocities into account for such applications. The problem is solved in the following
way: After reading the normal equation file, the system is expanded (station coordinate
parameters are added) according to a scheme illustrated in Figure 9.3. The resulting system
of normal equations is singular. But it is now possible to change the validity interval
according to Section 9.3.5. The length of the new interval covers the entire analyzed period
(e.g., one year). The resulting normal equation system may then be stacked together with
the other systems (transformed as described in Section 9.3.6). Stacking of many normal
equation systems referring to different epochs removes the singularity.
9.3.8.2 Changing the Parameter Representation for SINEX.
As mentioned, the Bernese GPS Software consistently uses offset parameters for (piecewise)
linear functions. However, the SINEX standard (see Section 4.6) requires offsets and
drifts for Earth rotation parameters.
In Section 7.5.2 we gave the formulae for the transformation between these two approaches.
If we want to change the parameterization from offsets only to offsets and drifts, we have
to expand the normal equation system according to Figure 9.4.
After the expansion the pairs of offsets are transformed into offsets and drifts. The resulting
normal equation system is, of course, singular. The singularity is removed if continuity at
the interval boundaries is imposed by applying constraints.
x
x i
x i+1
t
Figure 9.4: Normal equation system expansion for SINEX.
x
x
t 1
x i
x i
t 2
x 2
x i+1
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t