Bernese GPS Software Version 5.0 - Bernese GNSS Software

14. Clock Estimation
τ (BRUS-PTBB)
100 s 1000 s 10000 s
Interval
Legend:
Observation types used
original code only
smoothed code only
smoothed code and phase
phase only
Figure 14.1: Allan variance for the time transfer between PTBB and BRUS for day 03-
1390 of the example campaign using original code, smoothed code, and phase
observations for the clock estimation.
Precise Time and Frequency Transfer Using Phase Measurements
The phase observations are much more accurate than the code data. Therefore, it is preferable
to use them also for the estimation of clock parameters. The problem of using the phase
data for time transfer is a one-to-one correlation between the clock parameters (cδk and cδi )
and the initial phase ambiguity λn i k
which is evident from the observation equations (2.34).
This correlation prevents the direct access to the clock parameters if only carrier phase
measurements are used. As a consequence the initial phase ambiguity parameter n i k absorbs
the mean reading of the clock averaged over the measurement resp. analysis time interval. It
is the change of the clock values with respect to a reference epoch which can be estimated
from carrier phase observations only because the initial phase ambiguity cancels out by
differencing measurements from successive epochs. This means that carrier phase alone can
be used for frequency transfer only as long as phase ambiguities are connecting the epochs.
On the other hand the pseudorange measurements have a direct access to the clock parameters.
It is, therefore, possible to use both observation types in a combined data analysis. The
different accuracy level of the two measurement types are taken into account by weighting
the data in the parameter estimation procedure.
The same fact may also be explained in another way: In the observation equations the
correction of the receiver (and satellite) clocks with respect to GPS system time δi (δ k )
contain not only the difference of the clock to the GPS time but also the hardware delays 1 .
These delays may be different for pseudorange and phase observations. In the case of time
transfer – i.e., when comparing two receiver clocks – the hardware delays for a satellite
cancel out if it was observed from both stations at the same epoch.
In a time transfer solution using only the carrier phase observations the hardware delays will
be absorbed by the initial phase ambiguities. For a pure pseudorange solution, on the other
hand, the hardware delays remain in the clock parameters. A combined solution using phase
and pseudorange observations is necessary (a) to compute the receiver clock parameters and
(b) to take advantage of the high accuracy of the carrier phase observations.
1 “Hardware delay” is used in the sense of the constant part of the clock parameters in the GPS observation
equations. It contains not only the real hardware delay – e.g., cable delays – but also a constant reading of
the receiver (satellite) clock. The two cannot be distinguished by analyzing GPS data without changing
the hardware configuration and additional measurements.
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