Global Positioning System Reference
In-Depth Information
= λ 1 ρ
m ( 1 )
1
2
3
4
5
6
7
8
9
10
11
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14
15
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26
27
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45
ϕ pq
ϕ pq
pq
k (t)
pq
k ( 1 )
pq
pq
km (R 2
R 1 , 1 )
km (R 2
R 1 ,t)
− ρ
m (t)
+ ρ
− ρ
λ 1 ρ
m (t)
pq
k
pq
2
(t)
− ρ
(7.114)
Equation (7.114) can be solved for x m ,given x k and observations to at least four
satellites (three double differences). Once the position of m is known, the ambiguities
can be computed from (7.110).
If the topocentric satellite distances did not change during the antenna swapping
due to motion of the satellites, the antenna swap technique would yield a baseline
vector of twice the actual length. The geometry of antenna swap can be readily
visualized in a simplified one-dimensional situation. Consider a horizontal baseline
and a satellite located somewhere along the extension of that baseline. As one antenna
moves from one end of the baseline to the other, it will register, let's say, a positive
accumulated carrier phase change equal to the length of the baseline. As the other
antenna switches location, it will also register a carrier phase change equal to the
negative of the length of the baseline. Both receivers together will register a motion
of twice the length of the baseline.
Initialization by antenna swap on the ground is conveniently done for a very short
baseline of a couple of meters. A typical point positioning solution for x k is sufficient
for such short baselines. See Equation (5.66) regarding the relationship between
accuracy requirements for x k as a function of the length of the baseline.
The initialization by antenna swap works for single- and dual-frequency receivers.
At the time it was introduced it represented a major move forward in making kine-
matic surveying attractive in practice because at the time, surveyors operated mostly
single-frequency receivers only. With dual-frequency receivers, all-in-view satellite
observations, and optimized algorithms that include such optimal integer estimators
as LAMBDA (to be discussed below), a baseline can be readily initialized without
an antenna swap. In fact, initialization, i.e., ambiguity fixing can even occur on-the-
fly (OTF) while the roving receiver is moving. Under the right conditions, i.e., dual-
frequency observation, many satellites visible, good antenna, etc. the ambiguities can
be fixed every epoch, making not only antenna swap obsolete but also masking the
difference between static and kinematic techniques. Including GLONASS satellites
will improve the reliability of epoch-by-epoch ambiguity resolutions, as will future
Galileo satellites and the addition of the L5 frequency to GPS, which is part of the
GPS modernization.
[27
Lin
0 ——
Sho
PgE
[27
7. 7.6 GLONASS Carrier Phase Processing
The GLONASS satellites transmit at different carrier frequencies as specified by
(3.91) and (3.92). Maintaining the notation introduced in Chapter 3 we use a su-
perscript to identify the GLONASS satellite frequency, using the channel number.
Since the GPS satellites use the same frequency, there is no need for this extra su-
perscript to identify GPS satellite frequencies. In general, the superscript q and s are
used to identify any of the S GPS GPS or S GLO GLONASS satellites, respectively. The
 
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