Tracking GPS Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 178

FIGURE 8.11 Digitized input signal and prompt code are 100 ns off.

the acquisition program has less sensitivity than the tracking program. From
experimental results it appears that as long as the acquisition program can find a
signal, the tracking program can track it without any difficulty.
In Equation (8.45), when x> 100 ns or x< − 100 ns, the prompt code and
the input data are misaligned by more than half the sampling time. Under this
condition, the input data should be shifted one sample to align better with the
code as shown in Figure 8.12. In this figure, before the data shifting the x is
larger than d /4 (or half the sampling time). All three codes, the prompt, early,
and late, move to the left, which is equivalent to shifting the input data to the right
as shown in Figure 8.12. After the shifting of input data, x is smaller than d /4.
When x = 100 ns, r = 0 . 705 calculated from Equation (8.45). When x =

− 100 ns, r = 1 . 419(1/0.705). These two r values (0.705 and 1.419) can be con-

sidered as a threshold. If the r value is less than 0.705 or larger than 1.419,
this means x> 100 ns of x<

− 100 ns. Under both conditions, the input data
should be shifted one sample to better align with the locally generated code. It is
impractical to use the r value from 1 ms of data to determine whether to make
a shift of the input data because of the noise. It usually takes 10 or 20 ms of
data to make a decision. From Section 3.6 and considering a 10 kHz Doppler
frequency shift on the carrier, it takes approximately 16 ms to shift the C/A code
by half the sampling time of 100 ns, which can justify this update rate.
In the actual tracking program used, the update is performed every 10 ms. The
r value is calculated every millisecond, but ten r values are averaged and the
averaged value is compared with the threshold to determine whether a shift in
input data is needed. The x value calculated from the averaged r value through
Equation (8.45) is considered as the fine time resolution.