Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 193

= 14.24 Hz 2 . If the maximum LOS jerk dynamics is 10 g /s = 98 m/s 3 , then this trans-

lates into d 3 R / dt 3 185,398°/s 3 for L1. Substituting

these numbers into (5.20) results in a maximum dynamic stress error of f e

10 6 /c

= 98 × 360 × 1,575.42 × =

=

50
Hz, the FLL noise bandwidth is acceptable. Figure 5.26 illustrates the FLL thermal
noise tracking jitter and tracking thresholds, assuming a second-order loop under
10 g /s jerk dynamics with typical noise bandwidths and predetection integration
times.
Figure 5.27 illustrates the jerk stress thresholds for a second-order FLL as a
function of noise bandwidth with ( C / N 0 ) dB as a running parameter. Comparing the
thresholds in Figure 5.27 for the second-order FLL with those of Figure 5.25 for a
third-order PLL, notice that the FLL has much better dynamic stress performance
than the PLL at the same noise bandwidths and C / N 0 . For example, at 10 Hz and 35
dB-Hz, the FLL can tolerate up to 240 g /s while the PLL can only tolerate up to 4 g /s.
The spread is much smaller for weaker C / N 0 . The PLL would have performed mod-
erately better under dynamic stress if the predetection integration time had been
reduced from 20 ms to 5 ms, as was the case for the FLL. This comparison reinforces
the earlier statements that a robust GPS receiver design will use an FLL as a backup
to the PLL during initial loop closure and during high dynamic stress with loss of
phase lock but will revert to pure PLL for the steady state low to moderate dynamics
in order to produce the highest accuracy carrier Doppler phase measurements. Also
note that the maximum predetection integration time for FLL with C/A code or P(Y)
code is 10 ms, since two samples within one data transition interval are required for
the FLL discriminator.

185,398/(14.24 × 360) = 36 Hz. Since the 3-sigma threshold is 1/(4 × 0.005) =

Bandwidth, predetection integration time, jerk
2 Hz, 10 ms, 0.01 g/s

2 Hz, 10 ms, 0.01 g/s 10 Hz, 5 ms, 1 g/s 10 Hz, 5 ms, 1 g/s 18 Hz, 2 ms, 10 g/s

50 50

45 45 41.7 Hz threshold forT=2ms

40 40

Frequency = 1,575.42 MHz

35 35

30 30

25 25

16.7 Hz threshold forT=5ms

20 20

15 15

8.3 Hz threshold forT=10ms

10 10

5 5

0 0

15 15 17 17 19 19 21 21 23 23 25 25 27 27 29 29 31 31 33 33 35 35

( / CN 0dB ) (dB-Hz)

Figure 5.26 Total FLL jitter for second-order carrier loop.