Global Positioning System Reference
In-Depth Information
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
The ionospheric refractivity is
f
N
40
.
30
f
2
=
2
f
2
+··· =
N
I
N
e
1
(6.64)
Th
e total electron content (TEC) along the path from receiver to the end of the
ef
fective ionosphere is
N
e
ds
TEC
=
(6.65)
The TEC represents the number of free electrons in a 1-square-meter column along
the path and is given in units of [el/m
2
].
[21
6.5 IONOSPHERIC CODE DELAYS AND PHASE ADVANCES
Lin
—
-
——
No
*PgE
We need to deal with the phenomena of carrier phase advancement and group delay of
the codes due to the ionosphere. As an introduction to the propagation in a dispersive
medium, we consider the simplified situation of wave propagation in a homogeneous
and isotropic medium. In a homogeneous medium, the index of refraction is constant
and the isotropic property implies that the propagation velocity at any given point
in the medium is independent of the direction of the propagation. In such medium a
harmonic wave with unit amplitude is described by
t
x
c
ϕ
[21
ϕ
=
cos
ω
−
(6.66)
The symbol
t
denotes the time,
c
ϕ
[m/sec] is the phase velocity (propagation speed
of the wave), and
x
is the distance from the transmitting source. The angular fre-
quency
ω
[rad/sec], the frequency
f
[Hz], the wavelength
λ
ϕ
[m], and the wave number
k
[rad/m] (phase propagation constant), are related by
ω =
2
π
f
(6.67)
c
ϕ
f
λ
ϕ
=
(6.68)
2
π
λ
ϕ
k
=
(6.69)
Using the relations (6.67) to (6.69) the wave equation (6.66) can be written as
ϕ
1
=
cos
(
ω
t
−
kx)
(6.70)
Let us consider another wave that has a slightly different frequency and wave number,
