Bernese GPS Software Version 5.0 - Bernese GNSS Software

14. Clock Estimation
14.1 Introduction
According to the observation equations (2.34) the terms cδk and cδ i are defined as the
correction of the receiver and satellite clocks with respect to GPS time. For most of the
applications these parameters are a huge number of uninteresting unknowns. By forming
double-differences of the observations (see Eqns. (2.37)) the clock parameters are eliminated.
Other applications such as time transfer using the GPS require that these clock parameters
are estimated instead of being pre-eliminated by forming double-differences. If, e.g., some
of the receivers (k and ℓ) in the network are connected to “well defined” clocks (e.g., at
time laboratories) the estimated clock parameters may be compared (δk −δℓ). If the internal
receiver clock for which the clock parameters δk are estimated can be measured with respect
to another clock or to UTC(k) of the time laboratory the difference UTC(k)−UTC(ℓ) can
be obtained for each epoch where clock parameters are estimated. In a network solution all
contributing clocks can be compared in this way epoch by epoch. If the internal receiver clock
is driven by an external clock but the difference is unknown (but constant) the estimates
for the receiver clock δk can be used for frequency transfer.
Together with the receiver clocks the satellite clock parameters are estimated, too. In this
way you get a consistent set of receiver and satellite clocks for each epoch. The satellite
clock corrections are interesting, e.g., for a precise point positioning (PPP, see Section 10.5).
Introducing the satellite clocks together with the consistent orbit and ERP-information
the position (or epoch-wise kinematic positions) as well as the epoch-wise receiver clock
parameters of a single station may be computed. The results are consistent with the solution
that produced the satellite orbit, the Earth orientation information, and the satellite clocks.
Only differences between receiver and satellite clock parameters (cδk − cδ i ) appear in the
observation equations (2.34). It is, therefore, only possible to solve for the clock parameters
in a relative sense. Parameters for all but one clock may be estimated, i.e, either a receiver
or a satellite clock has to be kept fixed. Alternatively an ensemble of clocks may be selected
as a reference. Their sum of estimated clock corrections may be constrained using a zeromean
condition. The selected reference clock needs to be synchronized with respect to GPS
system time (see Section 2.3.5). If you fix more than one reference clock (e.g., all satellite
clocks in the case of a PPP) you must be sure that all these clocks are strictly consistent –
they have to originate from one solution.
Bernese GPS Software Version 5.0 Page 289