GPS Software Receivers - Fundamentals of Global Positioning System Receivers: A Software Approach - page 196

measured only in a relative way as shown in Figure 9.5, because the clock bias
of the receiver is an unknown quantity. In this figure the points represent individ-
ual input digitized data and they are separated by 200 ns because the sampling
rate is 5 MHz. The relative pseudorange is the distance (or time) between two
reference points. In this figure the beginning point of subframe 1 is used as the
reference point. All the beginning points of subframe 1 from different satellites
are transmitted at the same time except for the clock correction terms of each
satellite. As a result one can consider that the subframes from different satel-
lites are transmitted at the same time. Since the beginnings of subframe 1 from
different satellites are received at different times, this difference time represents
the time (or distance) difference from the satellite to the receiver. Therefore, it
represents the relative pseudorange. Subframe 1 occurs every 30 seconds and the
maximum time difference between two satellites is about 19 ms as discussed in
Chapter 3. From this information it is guaranteed that the subframe 1's transmit-
ted at the same time from different satellites are compared. In other words, if
the difference time between two satellites is in the tens of milliseconds range,
the two subframe 1's must be transmitted at the same time and they cannot be
separated by 30 seconds.
Now the digitized input data point corresponding to the beginning of subframe
1 must be found. This information can be obtained from three input data: (1) the
beginning points of the C/A code obtained from the tracking program with a
time resolution of 10 ms and accuracy of 200 ns as discussed in Section 8.12;
(2) the beginning of the first navigation data (simplified as the first navigation
data point) obtained from Section 9.3; (3) the beginning of subframe 1 obtained
through subframe matching as discussed in Section 9.4 with a time resolution
of 20 ms.
Figure 9.6 illustrates the relations among these three quantities. In
Figures 9.6a, b, and d the results are obtained from actual collected data, but
Figure 9.6c is artificially created for illustration. The upper part of the figure
represents the original input data with the first beginning of the C/A code in the
first 5,000 digitized input data points obtained from the acquisition program. The
rest of the beginnings of the C/A code are obtained from the tracking program.
In the bottom of the figure, the beginning of subframe 1 is given. These figures
are used to help find the beginning of subframe 1 in terms of the beginning of
the C/A code.
FIGURE 9.5 Relative pseudorange.