Bernese GPS Software Version 5.0 - Bernese GNSS Software

13. Differential Code Biases
Prominent examples for the second receiver class are: Rogue and old Trimble (4000) models.
The latest generations of Leica, Novatel, Trimble receivers belong to the third class
(providing C1 with a quality absolutely comparable to that of P1).
Well-established GPS/GLONASS-combined receiver models, such as Ashtech Z18,
Javad/Topcon, typically are P1/P2 receivers. However, we are already confronted with
GNSS receiver models that must be attributed to two classes: the new Trimble NetR5
behaves like a C1/P2 receiver for GPS and like a P1/P2 receiver for GLONASS.
13.1.3 Differences of Code Biases
Instrumental biases, BC1, BP1, BP2, are present with respect to C1, P1, P2. These biases
are not accessible (in the absolute sense). It is common to consider the following differences
of code biases:
• BP1 − BP2 = BP1−P2,
• BP1 − BC1 = BP1−C1.
BP1−P2, BP1−C1 are called differential code biases (or simply DCBs). BP1−P2 is addressed
in [GPS-ICD, 1993] as group delay, τGD (see also [Wilson et al., 1999]). The relation between
τGD and BP1−P2 may be given as
τGD = −1.55 · BP1−P2 + B0, (13.1)
where B0 is an arbitrary offset (irrelevant to our applications).
Figure 13.1 shows the order of magnitude of BP1−P2 DCB values for the current GPS satellite
constellation. These values are a by-product from the global ionosphere analysis performed
at CODE. The minimum-to-maximum value is about 13 nanoseconds (corresponding
to approximately 24 TECU). For the GLONASS satellite constellation, the minimum-tomaximum
value for the BP1−P2 DCB is, with about 22 nanoseconds, comparably big (see
Figure 13.2).
GPS BP1−C1 DCB values are shown in Figure 13.3. Compared with GPS BP1−P2 values,
the order of magnitude of BP1−C1 values is approximately 3 times smaller: the minimum-tomaximum
value is about 4 nanoseconds. Nevertheless, expressed in units of widelane cycles,
this corresponds to a maximum inter-satellite BP1−C1 DCB of 1.4 cycles!
Figures 13.1, 13.2, and 13.3 show, furthermore, that the individual PRN-specific DCB values
are rather stable in time. Note that the daily DCB retrievals are indicated with dots, the
30-day averages with circles. The day-to-day reproducibility is observed around 0.05 nanoseconds
rms (for satellite bias retrievals responding to BP1−C1). Finally, it should be stated
that it is common practice to impose a zero-mean condition on the set of DCB estimates
(with respect to each GNSS) for datum definition. This implies that DCB results may be
shifted by a common offset value, B0 (cf. Eqn. (13.1)).
It is worth mentioning that updated versions of Figures 13.1, 13.2, and 13.3 may be found
at http://www.aiub.unibe.ch/ionosphere/ [Schaer, 1998].
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