Tracking Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 284

where var represents variance and x i ( i = 1 : 5000) is 1 ms of input signal in

time domain.
The signal power is obtained from the frequency domain. As shown in
Figure 11.9b, the signal may disperse into several frequency bins. In practice,
it is difficult then to determine exactly the noise power. Thus, it is arbitrarily
decided that only 5 frequency bins, two on each side of the highest output, will
be used to measure the signal power. An additional requirement is that the out-
puts from the four neighboring frequency bins must be 3.5 times greater than
the noise amplitude (square root of noise power) to qualify as signal power. The
constant 3.5 is arbitrarily chosen. The reason for having this requirement is to
take into consideration the case where the signal is centered on one frequency
bin and the neighboring four frequency bins contain most of the noise. Under
this condition the neighboring bins should not contribute to the signal power.
The signal power P s can be calculated as

2

A(k) 2 P s = where

( 11 . 7 )

k =− 2

A(k) > 3 . 5 P n

A (0) is the highest output in Figure 11.9b, and A ( k ), k − 1, 1, and 2 are

the four neighboring bins. P n is noise power obtained from the previous equation.
Because the signal is measured in 1 Hz resolution, the S / N calculated through
this method is equal to C / N 0 . For normal signal strength, the S / N calculated from
second to second has a standard deviation of about 0.1 dB, based on processing
results of experimental data.

=− 2 ,

11.9 BASIC IDEA OF FINDING THE PSEUDORANGE ( 2 )

The idea of finding the fine time, which is related to pseudorange, is based on
the correlation output, as discussed in Section 8.11. The only difference is that
in Section 8.11 the fine time is calculated every ms, and the results from every
10 ms are averaged into one point. It appears that even for signals with normal
strength, the correlation output is rather noisy. For a weak signal it is practically
impossible to obtain a meaningful fine time from 1 ms of data. For this reason,
one second of data is used to find the fine time.
One ms of input data (5000 points) is used to generate three output points.
One is the compressed output, which is obtained by multiplying and summing the
input with the prompt code. The other two points are generated by multiplying
and summing the input with the early and late local codes. The generation of
the compressed output from the prompt code was discussed in Section 11.6. The
local early and late codes can be generated by shifting the 5000-point prompt
C/A code by one or two data points. In Section 8.11 the early and late codes
were obtained by shifting two data points; here they are obtained by shifting