Global Positioning System Reference
In-Depth Information
made by the receiver. This measurement is derived from the carrier-phase tracking
loop of the receiver. Mathematically, the relationship is as follows:
t
n
()
φφ
=
+
∫
f
τ
d
τ
+
φ
where
φ
=
A
l
1
l
1
D
r
11
l
1
n
n
−
1
l
1
l
1
0
n
t
(8.8)
n
1
t
n
()
φ
=
φ
+
∫
f
τ
d
τ
+
φ
where
φ
=
A
l
2
l
2
D
r
12
l
2
n
n
−
1
l
2
l
2
0
n
t
n
−
1
where:
is the accumulated phase at the epoch shown
l
1 and
l
2 are the link 1 and link 2 frequencies
n
and
n
1 are the current and immediately past epochs
f
D
is the Doppler frequency as a function of time
r
is the fractional phase measured at the epoch shown
A
l
1
,A
l
2
are whole plus fractional cycle count (arbitrary) at receiver acquisition
−
Even though the receiver carrier-phase measurement can be made with some
precision (better than 0.01 cycle for receivers in the marketplace) and any advance in
carrier cycles since satellite acquisition by the receiver can be accurately counted, the
overall phase measurement contains an unknown number of carrier-cycles. This is
called the carrier-cycle integer ambiguity (
N
). This ambiguity exists because the
receiver merely begins counting carrier cycles from the time a satellite is placed in
active track. If it was possible to relate
N
to the problem geometry, the length of the
path between the satellite and the user receiver, in terms of carrier cycles or wave-
lengths, could be determined with the excellent precision mentioned earlier.
Figure 8.11 depicts such a situation and also illustrates the effect of the calcu-
lated carrier-phase advance as a function of time (e.g.,
1
or
2
). Clearly, determining
N
for each satellite used to generate the user position is of paramount concern when
interferometric techniques are used. As the term interferometry implies, phase mea-
surements taken at two or more locations are combined. Normally, the baseline(s)
between the antennas are known, and the problem becomes one of reducing the
combined phase differences to determine the precise location of the source of the sig-
nal. In the case of relative DGPS, the baseline is unknown but the location of the sig-
nal sources (the GPS satellites sometimes referred to as SVs) can be precisely
determined using ephemerides available from the navigation data in the satellite
transmission.
8.4.1.3 Double Difference Formation
Generation of both carrier-phase and pseudorange (code) double differences (DDs)
is key to determining the baseline vector between the ground and airborne platform
antennas. In so doing, satellite ephemerides must be properly manipulated to ensure
that the carrier-phase and code measurements made at the two receiver locations
are adjusted to a common measurement time base with respect to GPS system time.
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