Geoscience Reference
In-Depth Information
Code pseudoranges
The measured time difference ∆
t
is affected by the satellite clock error
δ
S
and the receiver clock error
δ
. The error
δ
S
of the satellite clock can be
modeled by a polynomial with the coecients being transmitted in the nav-
igation message. Assuming the
δ
S
correction is applied, the time interval ∆
t
multiplied by the speed of light
c
yields the code pseudorange
R
and, hence,
R
=
c
∆
t.
(5-2)
Assuming a common time reference for satellite and receiver, e.g., GPS time,
the term ∆
t
may be decomposed into the run time ∆
t
(GPS) and the receiver
clock errors
δ
leading to
R
=
c
∆
t
(GPS) +
cδ
=
+
cδ,
(5-3)
where
is the geometric range between the satellite and the receiver. The
receiver module responsible for code pseudorange measurements is denoted
as delay lock loop (DLL). Details on the DLL functionality are given in Misra
and Enge (2001: Sect. 9.5).
Phase pseudoranges
Assuming again that the satellite clock error correction is applied, the phase
pseudorange Φ is modeled by
λ
Φ=
+
cδ
+
λN,
(5-4)
where the carrier wavelength
λ
has been introduced. The range
represents
the distance between the satellite at emission epoch
t
and the receiver at
reception epoch
t
+∆
t
. Phase measurements are ambiguous, since the initial
integer number
N
of cycles between satellite and receiver is unknown. As
long as the tracking of a satellite is not interrupted, the ambiguity remains
constant within the tracking loop of the receiver. The responsible receiver
hardware is denoted as phase lock loop (PLL). Compared to (5-3), the phase
pseudorange differs from the code pseudorange only by the phase ambiguity
term
λN
. Dividing the above equation by
λ
scales the phase to cycles.
As mentioned previously, the majority of navigation applications does not
need carrier phase measurements. Only for increased accuracy requirements
(e.g., relative positioning; see below), phase measurements become relevant.
Doppler data
Some of the first solution models proposed for GPS were to use the Doppler
observable. Considering Eq. (5-4), the equation for the observed Doppler
