The GNSS integer ambiguities: estimation and validation

2.2.3 Signal travel time
In the preceding two sections the signal travel time τ s r in equations (2.7) and (2.12) has
been assumed equal for code and phase measurements, as well as for measurements on
different frequencies. In reality, this is not true since the signal travel time of the code
actually is the group travel time. Moreover, the instrumental delays and atmospheric
effects are different for the code and phase observations and for different frequencies.
The difference between the travel times of different observation types and frequencies is,
however, less than 10 −7 s corresponding to sub-millimeter satellite position differences
(Teunissen and Kleusberg 1998). Therefore, the travel times of all observation types are
considered equal here.
2.2.4 Instrumental delays and clock errors
The receiver and satellite clock errors are independent of the observation type. On the
other hand, the instrumental delays are different for code and phase measurements and
for different frequencies. Still, the instrumental delays and clock errors will be lumped
together because it is not possible to separate the effects in a least-squares adjustment.
Hence:
dtr,j(t) = dtr(t) + dr,j(t)
dt s ,j (t) = dts (t − τ s r ) − d s ,j (t − τ s r )
δtr,j(t) = dtr(t) + δr,j(t)
δt s ,j (t) = dts (t − τ s r ) − δ s ,j (t − τ s r )
2.2.5 Atmospheric delays
(2.13)
GNSS signals have to travel through the earth’s atmosphere on their way from satellite
to receiver. In the atmosphere neutral atoms and molecules, and charged particles
are present that interact with the signals. This causes a propagation delay and signal
absorption. The latter effect is not considered here. The propagation delay is caused
by a deviation of the propagation speed from the velocity of light in vacuum, and an
indirect delay due to signal bending. The delay is indicated with da and δa in equations
(2.7) and (2.12) respectively.
The atmosphere can be divided in different ”layers” with different characteristics. For
GNSS especially the propagation characteristics are important, which means that the
atmosphere needs to be divided into two ”layers”: the troposphere and the ionosphere.
Tropospheric delays
The troposphere is the lower part of the earth’s atmosphere and ranges from the surface
to a height of approximately 9 km at the poles and to 16 km at the equator. In the
troposphere neutral atoms and molecules are present, which cause a signal delay. The
troposphere is a non-dispersive medium at the GNSS frequencies, which means that
10 GNSS observation model and quality control