Global Positioning System Reference
In-Depth Information
thus the result is a complex quantity and represented by
y
es
. Similarly the com-
pressed late outputs are summed to form one point and represented by
y
ls
.The
amplitudes of
y
es
and
y
ls
are referenced as
y
esa
and
y
lsa
, respectively. These are
the quantities shown in Equation (11.8). The actual summation method will be
explained in the next section.
11.10 OBTAINING THE SUMMED EARLY AND LATE PEAK
CORRELATION OUTPUTS (Y
es
AND Y
ls
)
First, the approach to obtain
y
es
and
y
ls
will be presented. Then their meaning
will be explained. Since the explanations for both
y
es
and
y
ls
are identical, only
y
es
will be used for illustration.
Every ms an early peak correlation result
y
e
is generated. Because the carrier
frequency is a complex quantity, after frequency conversion the output is also
complex. As a result the early peak correlation
y
e
is also complex. In one second,
1000
y
e
values are generated. These values are summed together in complex form
rather than in absolute value, and the result is referred to as
y
es
. Summing in
complex form is equivalent to coherent processing. The next step is to discuss
the meaning of
y
es
.
In order to simplify the discussion, a numerical example will be used. If the
Doppler is 5 kHz, it causes the time shift in every digitized input data sam-
ple by
−
6
.
3475
×
10
−
13
sec, which has been discussed in Section 11.5 and
Equation (11.2). Every ms the time shift is
−
×
10
−
9
sec (
−
6
.
3475
×
3
.
174
10
−
13
5
,
000). Let us assume that the initial prompt C/A code matches the
input signal exactly. Then the amplitude of the prompt peak correlation output
will be 1023. The early and late C/A code will mismatch the input signal by
one sample with correlation peaks of 813.7. Because the sampling interval is
200 ns, the next ms the early C/A code will mismatch the input by 196.826 ns
(200
−
3
.
174 ns), and the corresponding peak correlation output will be slightly
higher than 813.7. After 20 ms the early code and the input signal will be mis-
matched by about 136.53 ns (200
−
3
.
17375
×
20
=
200
−
63
.
475). Thus the
early correlation peak at 20 ms is even higher than that at the beginning of the
input. The amplitude of the early output
y
e
is shown in Figure 11.10.
The initial output shown in the figure is represented by the solid line and the
final output (20 ms later) by the dotted line. The outputs from the prompt and
the late are decreased because the mismatch increases by 63.475 ns after 20 ms.
The amplitude of
y
e
from each ms is shown in Figure 11.11. This figure can be
considered a magnified version of
y
e
shown in Figure 11.10. After 20 ms the
prompt local C/A code is regenerated and it matches with the input again. Thus,
the amplitude of
y
e
decreases to the same initial value. As time goes on, this
mismatch decreases again. This process repeats every 20 ms, or in 1 second it
occurs 50 times. The results of the prompt peak correlation
y
p
and the late peak
correlation
y
l
can be explained the same way.
The summation of these
y
e
will be referred to as
y
es
. From Figure 11.11
one can see that the result is the average value between the beginning and the
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