Global Positioning System Reference
In-Depth Information
are referred to as
y
esa
,
y
psa
,and
y
lsa
, respectively and they can be obtained by
the following equation:
n
=
1
y
e
(n)
n
=
1
y
p
(n)
n
=
1
y
l
(n)
1
,
000
1
,
000
1
,
000
y
es
=
y
ps
=
y
ls
=
(
11
.
9
)
y
esa
=|
y
es
|
y
psa
=|
y
ps
|
y
lsa
=|
y
ls
|
where
y
e
(n)
,
y
p
(n)
,and
y
l
(n)
are the 1 ms early, prompt, and late correlation
peaks, respectively;
y
es
,
y
ps
,and
y
ls
are the 1 second early, prompt, and late
correlation peaks, and
y
esa
,
y
psa
,and
y
lsa
are their corresponding amplitudes,
respectively.
The
y
esa
,
y
psa
,and
y
lsa
are three points approximately at the middle between
the initial and final points of
y
e
,
y
p
,and
y
l
, respectively. Figure 11.11 also shows
the position of
y
esa
. From this discussion it is obvious that the summation does not
change the meaning of
y
e
,
y
p
,and
y
l
, as presented in Section 8.11. The advantage
is that the
S
/
N
is enhanced, and Equation (11.8) provides the desired fine time.
This fine time is different from the fine time calculated in Chapter 8. The fine
time calculated in Chapter 8 is from 1 ms of data, and the result represents the
fine time of that 1 ms. The fine time obtained through Equation (11.8) is from 1
second of data, and the fine time is referred to the first C/A code initial phase in
one second of data. This quantity can be related to the fine time at every ms, and
the fine time of a certain ms can be calculated from the time delay caused by
the Doppler frequency. The following example shows how to find the fine time
of the first ms of data.
In this example the local C/A code and the C/A code in the input data are
assumed exactly matched for the first ms. However, there might be a slight error.
The fine time obtained from 1 second of data is used to find this error because 1
second of data should provide better accuracy. For example, at the beginning of
the second ms the mismatch is 3.174 ns for a Doppler frequency of 5 kHz. At
the twentieth ms the mismatch is 60.306 ns (3
.
174
×
19), and we let this quantity
be represented by
t
. Thus the average fine time calculated should be 30.153 ns,
which is half of
x
(or 60.306) ns, marked as
x
/2 in Figure 11.10. If measured
at 30.153 ns, the fine time implies that the local C/A code and the C/A code
of first ms are perfectly matched, as assumed. If the measured fine time is not
equal to 30.153 ns, the difference between measured
x
/2 and 30.153 represents
the misalignment between the local C/A and the C/A codes in the first ms. This
misalignment can be used to determine the true fine time of the first ms. The rest
fine times can be obtained from the first ms fine time and time shift (3.174 ns)
between adjacent ms.
It should be noted that in Equation (11.8) the value of
y
psa
is not used in
determining the fine time. The values of
y
psa
are the power level used to determine
the navigation data and carrier frequency, as discussed in Section 11.7. Thus a
high value of
y
psa
is desirable.
If the three local codes are generated every ms, then theoretically the locally
generated prompt C/A code and the C/A code in the input data can be matched
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