The influences of the clock errors on the GPS may be grouped into three types. One is factorised with the speed of light, c. Another is factorised with the speed of satellites. And the third is factorised with the working frequency.
The influence of the first type of clock error is obvious. For code measurements, one measures the transmitting time of the signal and multiplies the transmitting time with c to obtain the transmitting path length. A clock error of
will cause a path length error of
Similarly, a clock error of
will cause a phase error of 
Because of the factor c, a small clock error may cause a very large code and phase error. Therefore, high quality clocks have to be used on the satellites and receivers. Meanwhile, clock errors must be carefully modelled. A simple model may be expressed as
where b is the bias, d is the drift and a is the acceleration of the related clock. Time interval
is the valid period of clock error polynomial. The length of the interval depends directly on the stability of the clock. Such a model describes that the clock has a small drift and acceleration, and the drift and acceleration as well as bias are stable ones. The interval may be estimated by using the drift and acceleration accordingly.
In the case of SA (selective availability, for details cf. Sect. 5.7), the frequency of the clock on the satellite is manipulated artificially. In other words, the scale of the clock on the satellite is not any more a constant; i.e., the clock is not any more stable. Therefore in such a case, the model of Eq. 5.163 is not good enough for use. An alternative model of the clock error of the satellite in the case of SA is
That is, the clock bias has to be modelled for every measuring epoch. The clock error parameters have to be determined or equivalently eliminated every epoch.
The influence of the second type of clock error is more or less implicit. Recalling the code and phase models discussed in Chap. 4, there is a geometric distance between the satellite at the signal emission time and the receiver at the signal reception time. The position and velocity of the satellite are functions of time. Therefore, a clock error causes a computing error of the position of the satellite by vs8t, where vs is the velocity vector of the satellite. These errors pass through the distance function and cause errors of the computed distance. Such an influence is implicitly presented in all the GPS observation models and cannot be eliminated through forming differences. However, the influence of the clock error is factorised by the velocity of the satellite (about 3 km s-1), so an estimation of St up to an accuracy of 10-6 would be enough to ensure the needed accuracy of the computed satellite position. Usually, such an estimation is made through the single point positioning of every station at the every epoch (details cf. the section of single point positioning in Sect. 9.42). Of course, we must also take the relativistic effects into account.
As discussed above, the clock error causes a phase error of cSt/X; this is equivalent to a frequency error of fSt. It is obvious that this correction has to be taken into account in Doppler data processing.
Synchronisation of the clocks on the satellites and receivers is a basic prerequisite of a meaningful GPS measurement. Clock modeling leads automatically to the synchronisation of all clocks.
A recent study showed that the clock error parameters are linearly correlated with the ambiguity parameters (for details, see Sect. 9.1).
