Tracking Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 293

TABLE 11.2 Fine Time Measured by Simulated
Tracking Signals (One C/A Code used/sec)

Mean
Error (ns)

Standard
Deviation (ns) C/N 0

25 − 1.1 14

24 − 2.1 16

23 − 2.9 18

22 − 7.5 20

− 6.5

21 22

−

20 3.2 27

19 1.3 30

18 4.3 35

Because the number of runs used in obtaining Tables 11.1 and 11.2 is rather
small, it is difficult to draw a firm conclusion. From these limited data, how-
ever, one can see that the results are comparable. Theoretically the approach in
Section 11.11 should have a smaller mean error because in this method the y esa
and y lsa may not be equal. It is possible, however, to generate the C/A code
every second and make y esa and y lsa of about the same amplitude. Under this
condition the results from these two approaches should be very close.

11.13 TRACKING OF SIGNALS WITH NON-INTEGER SAMPLING
FREQUENCY ( 4 )

Non-integer sampling frequency means that in 1 ms, the C/A code sample gener-
ated is not an integer number. Strictly speaking, the number of digitized data per
ms can hardly be an integer. For example, in the preceding discussion the sam-
pling frequency was assumed to be 5 MHz, and the frequency was rather accurate.
In integer signal tracking, one can assume that each ms of data contains 5000
digitized points and the round-off error is small. However, if the sampling fre-
quency is off by 500 Hz, the sampling frequency becomes 5,000,500 Hz. With
this sampling rate, 1 ms of data would thus contain 5000.5 samples. This is
referred to as non-integer sampling frequency. In Section 11.11, it was assumed
that the locally generated C/A code and the input C/A are matched within 100 ns
(half the sampling time) at the end of 20 ms. If the mismatch, after a few ms,
is larger than half the sampling time, the sampling rate can also be considered
non-integer. When a non-integer sampling frequency is used, it has an impact on
the tracking program, and this is why the subject is discussed here.
In the preceding example the number of data points in 1 ms used in the
tracking program had to be truncated to an integer. Either 5000 or 5001 points
could be chosen. With either selection in the second ms, the locally generated
C/A code and the input signal are mismatched by half a sample time, or 100 ns.
In the third ms the mismatch will be one sample. It is obvious that this situation
does not fit the requirement for less than 100 ns of time shift after 20 ms.