Global Positioning System Reference
In-Depth Information
1023
1
1023
()
() (
)
∫
R
τ
=
GtGt
+
τ
d
τ
(4.22)
G
i
i
,
T
CA
t
0
where:
G
i
(
t
)
=
C/A code Gold code sequence as a function of time,
t
, for SVi
T
CA
=
C/A code chipping period (977.5 ns)
τ =
phase of the time shift in the autocorrelation function
The C/A code autocorrelation function is a series of correlation triangles with a
period of 1,023 C/A code chips or 1 ms, as shown in Figure 4.13(a). As observed in
Figure 4.13(a), the autocorrelation function of the GPS C/A (Gold) codes has the
same period and the same shape in the correlation interval as that of a maximum-
R()
G
τ
A
2
1
1023
−
0
τ
(seconds)
110
−
3
×
−
9
977.5
10
×
(a)
(
)
S( )
G
ω
10
−
9
ω
997.5
2
2
2
Envelope = A
sinc
A
2
ω
(radians)
2
π
−
9
977.5
×
10
(b)
(
)
G
2
S()
ω
P
S
10 log
0
−
20
dB
−
30
−
40
−
50
Line number
1
2
3
4
5
6
7
8
9
(c)
Figure 4.13
(a) The autocorrelation function, (b) spectrum, and (c) power ratio of a typical C/A
code.
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