Global Positioning System Reference
In-Depth Information
referencing is made to a non-physical reference station located in the vicinity of the
approximate position of the rover and virtual observations are generated to refer to this
non-physical reference station. The user typically has no information about the size of errors
and their behaviour. In contrast to the non-physical network approach, FKP and MAC
broadcast raw reference station observations and network information separately. The
network information is represented by dispersive and non-dispersive corrections and the
rover software decides how the network information is applied. A summary of these
methods is given in section 5.
Once the network errors are computed at the reference station, distance-dependent errors
need to be interpolated at the location of the user receiver. Several methods can be used for
such interpolation process including: the use of linear interpolation, using a linear
combination model, applying an inverse-distance linear interpolation or a low-order surface
model (used for example in the FKP technique), utilisation of the least-squares collocation
approach, or using Kriging techniques (see for instance Fototpoulos, 2000, Dai et al ., 2001,
Wu, 2009 and Al-Shaery et al ., 2010).
4. Estimation of the dispersive and non-dispersive errors at the network
reference stations
The mathematical equation of the code and phase observations for the receiver (j) and the
satellite (s) at time (t) can be written as:
G
s
j
G
R
G
s
s
s
s
s
()
s
() () ()
s
s
s
s
C
=
R
+
δ + δ −δ +
r (t
t)Tt
Tt It
−δ
It p
+ +ε
G
(1)
j
j
j
j
j
j
j
j
P j
s
j
R
G
s
j
G
R
G
c
s
s
s
s
s
s
s
s
s
s
s
φ =
R
+
δ + δ −δ +
r
c ( t
t) T(t)
T(t) I(t)
−δ
I(t)
+
N
+ +ε
p
G
(2)
j
j
j
j
j
j
j
j
i
φ
j
s
j
f
R
Where:
s
C,
s
φ
code and phase observations, respectively;
R G
s
j
geometric range between the user's antenna and the satellite;
δ G
s
r
orbit error;
c
speed of light;
δt j , δt s
receiver and satellite clock errors, respectively;
s
T (t)
modelled tropospheric refraction delay (mainly the hydrostatic, dry component of
the troposphere);
()
s
j Tt
δ
residual tropospheric refraction delay (mainly the unmodelled wet troposphere);
( )
s
j
I
t
modelled ionospheric refraction delay if applied (frequency dependent);
()
s
j It
δ
residual ionospheric refraction (frequency dependent);
f
signal frequency;
s
N
integer phase ambiguity;
s
p
s
j
total site dependent errors (antenna phase centre and multipath
δ
);
s
P ε ,
s
φ ε code and phase remaining random noise, respectively.
j
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