Global Positioning System Reference
In-Depth Information
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in addition to the station clock error, contains the common components of all the other
errors. The relevant portion of the pseudorange equations can now be written as
P
k
p
k
I
k,P
+ δ
T
k
cdt
p
= ρ
−
c
ξ
k
+
+ δ
(5.69)
The linearly dependent common components
ξ
k
in (5.68) cannot be estimated sep-
arately from the epoch point positioning solution but rather are absorbed by the
estimate of the receiver clock error
d
t
k
. Unmodeled errors that are common to all
observations at a particular station do not affect the estimated position. Thus, model-
ing of the ionosphere and troposphere, e.g., is useful only if it reduces the variability
with respect to the common portion.
Equation (5.68) also demonstrates how the requirements for positioning and tim-
ing with GPS are quite different. If the goal is to determine time, then modeling or
controlling the common station errors is of critical importance.
[18
5.
3.6.2 Relative Positioning
In relative positioning, the errors common to
bo
th stations tend to cancel during double differencing. For example, the tropospheric
co
rrection can be decomposed into the common station parts
T
k
and
T
m
and the
sa
tellite-dependent part as follows:
Lin
—
-5.
——
Nor
PgE
=
T
km
+
δ
T
m
−
T
km
+
δ
T
m
T
pq
km
T
k
T
k
− δ
− δ
(5.70)
=
δ
T
m
−
δ
T
m
T
k
T
k
− δ
− δ
It is useful to apply tropospheric and ionospheric corrections if the differential correc-
tion between the stations can be determined accurately. If this is not the case, because,
say, the meteorological data are not representative of the actual tropospheric condi-
tions, it might be better not to apply the correction at all and to rely on the common-
mode elimination. Because the ionosphere and the troposphere are highly correlated
over short distances, most of their delays are common to both stations. In terms of
the tropospheric effect, an exception to this rule might apply to nearby stations that
are located at significantly different elevations.
Because of the cancellation of most of the effects of the propagation media, the
clock errors, and hardware delays, relative positioning has become especially popular
and useful in surveying. Although the presence of the ambiguity parameters in the
double differences might initially be perceived as a nuisance, they provide a unique
vehicle to improve the solution if they can be successfully constrained to integers.
[18
5.
4 SATELLITE CODE OFFSETS
According to the ICD-GPS-200C (2000), the P1 and P2 codes are offset by
T
GD
.
This offset is also referred to as the differential group delay (DGD) or more generally
the differential code bias (DCB) for P1 and P2. The purpose of this delay is to allow
dual-frequency users to conveniently eliminate the ionospheric effect on pseudorange
observations when computing positions. This aspect is treated in detail in Chapter 7.
