Tracking Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 292

codes are off by half the sample time or 100 ns. For this example the local
C/A code needs a shift after 32 ms of data. In 32 ms the total time mismatch
is 32). The time shift step can only be 200 ns. After a

shift of 200 ns the mismatch becomes 98.432 ns (200

− 101.568 ns ( − 3 . 174 ×

101 . 568); thus, the next
shift will take about 63 ms because the fine time will change from 98.432 ns to
about − 100 ns, which is close to 200 ns. The time required for this time shift
can also be calculated as 200/3 . 174 ≈ 63 ms. In this approach, the mismatch of
every ms must be accumulated. If the mismatch is over ± 100 ns, a data point
shift will be needed. Figure 11.14 shows three lines of the ms y e values.
In Figure 11.14 the first line has 32 y e values, and the rest of the lines have
63 y e values. All three lines of y e 's should be one on top of the other, but to
show the delay time between them, they are drawn separately. There should be
about 17 lines in one second of time. The starting points of the lines are not at
the same time, as shown in Figure 11.11. The first line contains 32 y e 's. The next
15 lines each contains 63 y e 's. The last contains 23 y e 's. In order to obtain the
fine time through averaging, all the 1,000 individual fine times must be tracked.
The tracking of the fine time at every ms will be discussed in the next section.
As will become clear in the next section, the tracking of a signal with inaccurate
sampling frequency is a more general case than this one. Similarly the y l 's will
be shifted in identical time with the y e 's. Once the summations of y e 's and y l s are
obtained, the averaged fine time can be obtained in the same way, as discussed
in Section 11.10.
Simulated data were used to evaluate the results. For each S / N , 100 runs with
different noise sequence are performed. The results are listed in Table 11.2 ( 3 )

−

63 y e after 2nd time shift

63 y e after 1st time shift

Ending
of 32 y e

Beginning
of 32 y e

Time

FIGURE 11.14 Early correlation peak y e values with time shift.