Global Positioning System Reference
In-Depth Information
FIGURE 8.10
Correlation output of a C/A code.
The units of
x
and
d
are measured in chip time at 977.5 ns. The ratio of
y
l
and
y
e
can be written as
y
l
y
e
=
1
−
x
−
d
1
+
r
≡
or
−
x
d
(
1
−
r)(
1
−
d)
1
x
=
(8.45)
+
r
The value
x
can be found from this equation once
r
and
d
are calculated.
The value of
r
can be found from
y
l
and
y
e
, as shown in the first portion
of Equation 8.45. The above calculations are performed every 5,000 data points
(1 ms),
or
approximately
1
C/A
code
when
Doppler
shift
is
taken
into
consideration.
Now let us find the amplitude of
y
p
under the worst mismatched condition.
This information can show the sensitivity degradation of this approach. Under
the worst mismatched condition, the closest digitized point is 100 ns from the
beginning of the C/A code as shown in Figure 8.11. Since
x
=±
100 ns and
=
400 ns, after normalizing
x
to the chip time, one can find that
y
p
≈
1023
×
d
×
log(918.35/1023)) below the ideal correlation peak. Therefore, the worst situation
is that the correlation peak is about 1 dB less than the ideal case. Occasionally,
the C/A loop will be off more than
d
/4, because the update is not performed
every millisecond and the noise in the data may cause error. In the conventional
tracking loop the C/A code is generated every millisecond with the initial phase
properly adjusted. Therefore, the locally generated C/A code can better match
the input signal with slightly higher peak than the BASS method. In general,
−
=
−
(
1
100
/
977
.
5
)
918
.
35 from Equation (8.44), which is about
0.94 dB (20
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