Global Positioning System Reference
In-Depth Information
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Similarly, changes in the baseline vector and ephemeris position are related by
p
m
d
x
p
ρ
·
d
b
=
b
·
(5.65)
These relations are usually quoted in terms of absolute values, thereby neglecting the
cosine terms of the dot product. In this sense, a rule of thumb for relating baseline
accuracy, a priori geocentric position accuracy, and ephemeris accuracy is
d
x
P
ρ
d
b
d
x
c
ρ
=
=
(5.66)
m
m
b
Eq
uation (5.66) shows that the accuracy requirements for the a priori geocentric
sta
tion coordinates and the satellite orbital positions are the same. The accuracy
re
quirement is proportional to the baseline length. This means that for short baselines
an
accurate position of the reference station might not be required and that the simple
po
int positioning might be sufficient. A 1000 km line can be measured to 1 cm if the
ep
hemeris errors and the geocentric location error can be reduced to 0.2 m, according
to
the rule of thumb given above.
The simplified derivation given in this section neglects the impact of the satel-
lit
e constellation on the geometry of the solution. The only elements that enter the
de
rivations are the baseline length and the receiver-satellite distance.
[18
Lin
—
-
——
Lon
PgE
5.3.6 Cancellation of Common Mode Errors
GP
S positioning benefits considerably from the fact that common-mode errors can
be
combined with other parameters or canceled at times. It has been pointed out in
de
tail how single and double differences reduce the effects of clock errors. Additional
de
tail is provided here for both point and relative positioning.
[18
5.
3.6.1 Point Positioning
Generally, the propagation media affects satellite
sig
nals as a function of azimuth and elevation angle. For example, in the case of the
io
nosphere we split the total effect into a station average component
I
k,P
and one that
is
a function of the direction of the satellite
I
k,P
,
δ
I
k,P
I
k,P
=
I
k,P
+ δ
(5.67)
Th
e tropospheric delay can be split in a similar manner. The receiver hardware delay
ca
n also be a common source of errors. It is even possible that the satellite clocks
co
ntain a common offset, e.g., an incomplete correction due to relativity. The common
co
mponents are combined with the receiver clock error into a new epoch parameter
ξ
k
, giving
I
k,P
c
T
k
c
−
d
k,P
c
ξ
k
=
d
t
k
−
−
(5.68)
The symbols for the ionosphere and the troposphere have no superscript
p
in (5.68) to
indicate the common component. The symbol
ξ
k
represents a new unknown, which,
