Global Positioning System Reference
In-Depth Information
The coefficient
c
2
is estimated as
c
2
=−
40.3
n
e
Hz
2
. Rewriting this yields
403
.
n
403
.
n
n
=−
1
e
n
=+
1
e
(7.12)
p
g
2
2
f
f
Using (7.9), the phase and group velocity are estimated as
c
c
v
=
v
=
(7.13)
p
g
40 3
.
n
40 3
.
n
1
−
e
1
+
e
2
2
f
f
It can be observed that the phase velocity will exceed that of the group velocity.
The amount of retardation of the group velocity is equal to the advance of the car-
rier phase with respect to free-space propagation. In the case of GPS, this translates
to the signal information (e.g., PRN code and navigation data) being delayed and
the carrier phase experiencing an advance, a phenomenon referred to as
ionospheric
divergence
. Importantly, the magnitude of the error on the pseudorange measure-
ment and the error on the carrier-phase measurement (both in meters) are
equal—only the sign is different. The reduction in the carrier-phase measurement
value due to the presence of free electrons in the ionosphere can be intuitively
explained as being due to the fact that the distance from crest to crest in the electric
field of the signal is lengthened for the portion of the signal path contained within
the ionosphere.
The measured range is
User
SV
∫
S
=
nds
(7.14)
whereas the LOS (i.e., geometric) range is
User
SV
∫
l
=
dl
(7.15)
The path length difference due to ionospheric refraction is
User
SV
User
SV
∫
∫
∆
S
=
nds
−
dl
(7.16)
iono
The delay attributed to the phase refractive index is
User
SV
User
SV
40 3
2
.
n
∫
e
−
∫
(7.17)
∆
S
=
1
−
ds
dl
iono p
,
f
Similarly, the delay induced by the group refractive index is
User
SV
User
SV
40 3
2
.
n
∫
e
−
∫
∆
S
=
1
+
ds
dl
(7.18)
iono g
,
f
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