Global Positioning System Reference
In-Depth Information
t 2
t 1
t 3
φ 1
φ 2
t 0
φ 3
SV orbit
N
N
N
N
User position
Earth
Figure 8.11
Carrier-phase geometric relationships.
Formation of the DD offers tremendous advantage because of the ultimate cancella-
tion of receiver and satellite clock biases, as well as most of the ionospheric propa-
gation delay. If the two antennas are located at the same elevation, the tropospheric
propagation delay will largely cancel as well. This is not the case if one of the anten-
nas is on an airborne platform, and thus the path delay due to the troposphere expe-
rienced at the two antenna locations differs based upon their altitude differential.
Carrier-Phase Double Difference
Figure 8.12 schematically depicts a simple GPS interferometer interacting with a
single satellite. The phase centers of two antennas are located at k and m , and b rep-
resents the unknown baseline between them. SV p is in orbit at a mean distance of
20,200 km, and we assume the paths of propagation between the satellite and
the two antennas are parallel. The lengths of the propagation path between SV p
and k (
Φ p )orSV p and m (
Φ p ), in terms of fractional and integer carrier cycles, are
as follows:
()
()
()
Φ
p
t
=
φ
p
t
φ
p
t
+
N
p
+
S
+
f
τ
+
f
τ
β
+
δ
k
k
k
k
p
k
iono
tropo
(8.9)
()
()
()
p
p
p
p
Φ
t
=
φ
t
φ
t
+
N S f
+
+
τ
+
f
τ
β
+
δ
m
m
m
m
p
m
iono
tropo
where:
k and m refer to the receiver/receiver antennas phase centers
p is the satellite signal source
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