Tracking Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 297

initial phase such that y esa and y lsa are approximately equal. The position (time)
calculated from this equation is

N

1
N

= +

x ε d n or

n = 1

( 11 . 13 )

N

1
N

ε = x − d n

n = 1

This is almost the same as the tracking method discussed in the previous
section. The only difference between this method and that discussed in the previ-
ous section is that the sample shifting can be very frequent. This is the tracking
used on the Motorola front end, and the result is satisfactory.

11.14 CASES WHERE AN INITIAL C/A CODE POINT MATCHES
THE 1 MS SELECTED DATA

For simplicity, the 5 MHz sampling frequency is used here. The input data are
processed in 5000 point (1 ms) blocks. In general, in 5000 points of data the initial
phase of the C/A code is somewhere in the middle, as illustrated in Figure 11.8.
If a certain satellite has a positive Doppler frequency shift, one C/A code length is
slightly less than 5000 points. In other words, the time between two consecutive
initial phases of the C/A code is slightly shorter than 1 ms. As a result each time
the 5000 input data points are grabbed, the numerical value of the initial C/A
code point decreases, or the initial C/A code point is moves toward the beginning
of the data, as shown in Figure 11.17. In this figure, in order to illustrate the
shifting of the initial C/A code point, the effect is exaggerated. Recall that in
Figure 11.4b, which shows a positive Doppler frequency, the length of the C/A
code is shortened. For a 5 kHz positive Doppler frequency shift, in 1 second
of input data, the length of the C/A code is shortened by about 3,174 ns, as
discussed in Section 11.12. It takes about 315 seconds (10 6 /3174) to shorten it
by 1 ms. In 315 seconds, one additional ms of data is collected. This requires
processing the 1 ms of data twice. In a different explanation, it takes 315 seconds
to move a initial C/A code point from the end to the beginning of the input
data set.
Although this occurrence is rare, eventually, the initial C/A code point starts
moving to the front of the input data and becomes closely aligned with the first
digitized data point. When this phenomenon occurs, the next C/A code phase
also becomes closely aligned to the beginning point of the next 5000 points, as
shown in Figure 11.17, blocks A and B . For simplicity, one can consider that in
input data block A there are two initial C/A code points: one at the beginning
and one at the end of the data. When this phenomenon occurs, the initial point