Tracking Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 290

Correlation peak

1023

y p

y e

y l

−1

1

Time

FIGURE 11.13 Tracking result from second 2 on.

one from local and one from input data, are aligned, at the 20th ms they will be
off by x . If the two C/A codes in the first ms is off by x /2, at the 20th ms they

will be off by x /2. This arrangement will produce a slightly higher output y p .
Based on this idea, after the first second, the mismatch time x 0 can be found.
Since x 0 is known, in the next second the offset time can be chosen to any
desired value. In the present approach the next second instead of matching the
locally generated C/A code to the C/A code of the input signal, it is offset by
−

−

30.153 ns). The result is shown in Figure 11.13. The shaded area
represents the prompt peak correlation output. Comparing with the result in
Figure 11.10, where the C/A codes are aligned in the first ms, the prompt peak
correlation output from the present is slightly higher. With this arrangement, if
x is measured correctly, the beginning position of y p is off by

x /2 (or −

30.153 ns and
the ending position is off by 30.153 ns. Under this condition the average time
off is about 0 ns. The corresponding average amplitude loss is about 0.14 dB,
which can be calculated by assuming the average amplitude is 15.77 ns (30.153/2)
away from the correlation peak. The outputs from y esa and y lsa have the same
amplitude. Once this relation is obtained the rest of the tracking can follow the
same pattern.
This arrangement can also be used to better calculate the fine time, which
might be a more important factor. Equation (11.8) or (8.45) is based on the
assumption that the correlation peak is a triangle. As discussed in Section (8.12),
however, due to the limited bandwidth of the receiver, the correlation peak is not
a triangle. The exact shape of the correlation output is unknown. Therefore the
result calculated from Equation (11.8) can only be considered an approximation.
However, even if the correlation output shape is unknown, the fine time can be
calculated very accurate, if the values of y esa and y lsa are equal. If the multipath
effect can be mitigated, the correlation output shape can be considered symmet-
rical. Under this condition, if y esa equals y lsa , the fine time will be zero, which

−