Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 269

This same method is used in the tracking program to find whether there is a
navigation data transition every 20 ms.

Step2 . In determining the location of the data transition many data transitions
are needed. In this step the existence of data transition must be detected. Perform
correlation on 1 second of data points using the method mentioned in step 1 and
there should be about 1000 outputs. It is assumed that the highest output is near a
data transition. From this output every 20 points (20 ms) is checked to determine
whether there is a data transition. At the desired point, three points are averaged.
If the result is greater than zero, there is a data transition. For example, if the
highest output in one second of data is at location 108, then the points 8, 28, 48,
68, 88, 128, 148, ... , will be checked for data transition. At every point, three
points are averaged, such as at point 88 where the results at 87, 88, and 89 are
averaged together. If the averaged value is greater than zero, a data transition is
declared. If the averaged value is less than zero, no data transition is detected.
A total of 20 data transitions are needed to find the exact location of the data
transition. Once 20 possible transitions are found, the following steps are used
to determine the exact location.

Step3 . Using the example above, if the data transitions are found at 28, 88, 108,
128, ... , the points around these points will be selected. The center point with ± 9
points is selected. Nineteen points are selected with center at the transition point.
For example, points 19 - 37, 79 - 97, 99 - 117, 119 - 137, ... , are selected. There
are 20 groups and each group contains 19 points. The points in the groups are
added together, such as 19

+ 79 + 99 + 119 + ... ,20 + 80 + 100 + 120 + ... ,

... , and the result has 19 values. The highest value
is the location of the data transition.
The preceding approach was tested with simulated data. One second of data
was generated and every 40 ms had a data transition. The method could detect
20 data transitions and use the result to obtain the location. It should be noted
that some true data transition may be missed, and some false data transition may
be detected. Three different C/N 0 values were evaluated. Each case was tested
1000 times with a different noise sequence. The results are shown in Table 10.6.
It is interesting to note that when the C/N 0 changes by one dB, the result does
not change rapidly. It might be that the results were obtained from averaging over
a long record of data and the noise effect is reduced. Once the exact location

... 37 + 97 + 117 + 137 +

TABLE 10.6 Probability of First Data Transition Error

C/N 0 (dB) 25 24 23

Probability of error
in percentage

0.5 1.2 3.3