Global Positioning System Reference
In-Depth Information
FIGURE 8.9
Input signal, prompt, early, and late codes.
Figure 8.9 shows the prompt C/A code, which starts from data point 1 to
5,000. The early code is generated by shifting two points that are arbitrarily
chosen, 4,999 and 5,000, to the front; thus, the early code has the data points in
the sequence of 4,999, 5,000, 1, 2
...
4,998. Shifting points 1 and 2 to the end
generates the late code; thus, the late code has the sequence of 3, 4,
...
5,000,
1, 2. All three codes are correlated with the input signal.
The other approach uses five signals: one prompt, two early, and two late
signals. Shifting the prompt signal by 4 points generates the additional early and
late signals. Both approaches use approximations. A detailed discussion will be
presented in the following sections.
8.11 FINE TIME RESOLUTION THROUGH IDEAL CORRELATION
OUTPUTS
(
8
)
As discussed in Section 5.7, the correlation peak of the C/A code is 1,023. If the
C/A code is off by more than one chip, the correlation has three values: 63,
−
1,
65. The first method assumes that the correlation value is 0 if the two signals
are off by more than one chip for simplicity. Figure 8.10 shows the correlation
within one chip.
Each chip is 977.5 ns (1,000 us/1023) long without considering the Doppler
effect; let us refer this as the chip time. The three correlation values are:
y
p
from
the prompt C/A code,
y
e
from the early code, and
y
l
from the late code. The time
d
is measured from the prompt to the early or to the late in units of chip time.
For this special case, the time between the early and prompt or late and prompt
is 400 ns, which can be written in units of chip time as
d
=
.
4092 (400/977.5).
Suppose that
y
p
is
x
seconds from the ideal peak. This method uses the values
of
y
e
and
y
l
to find the value of
x
, which can be either positive or negative.
The value of
x
can be found from the following equations as
y
p
=
1023
(
1
−|
x
|
)
y
l
=
1023
(
1
−
−
x
d)
y
e
=
1023
(
1
+
x
−
d)
(8.44)
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