Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 192

5.6.2 FLL Tracking Loop Measurement Errors
The dominant sources of frequency error in a GPS receiver FLL are frequency jitter
due to thermal noise and dynamic stress error. The rule of thumb for tracking
threshold is that the 3-sigma jitter must not exceed one-fourth of the frequency
pull-in range of the FLL discriminator. As observed in Figure 5.11, the FLL
discriminator pull-in range is 1/ T Hz. Therefore, the general rule of thumb for FLL
tracking threshold is:

3 σ = 3 σ + f ≤ 1 4 T (Hz) (5.17)

FLL tFLL e

where:

3 σ tFLL = 3-sigma thermal noise frequency jitter

f e = dynamic stress error in the FLL tracking loop

Equation (5.17) shows that the dynamic stress frequency error is a 3-sigma
effect and is additive to the thermal noise frequency jitter. The reference oscillator
vibration and Allan deviation-induced frequency jitter are small-order effects on the
FLL and are considered negligible. The 1-sigma frequency jitter threshold would be
1/(12 T ) 0.0833/ T Hz.

The FLL tracking loop jitter due to thermal noise is:

=

FB
CN

4

1 1

σ =

n

1 + (Hz) (5.18)

tFLL

2 π T TCN

0 0

λ
π

FB
CN

4

1

σ =

L n

1 + (m s) (5.19)

tFLL

2 T TCN

0 0

where:

F = 1 at high C / N 0

= 2 near threshold

Note that (5.17) is independent of modulation design and loop order. It is inde-
pendent of L-band carrier frequency if the error units are expressed in hertz.
Because the FLL tracking loop involves one more integrator than the PLL track-
ing loop of the same order, the dynamic stress error is:

n n + 1

d
dt

1
360

dR
dt

1
360

dR
dt

f = = (Hz) (5.20)

e

n n n n + 1

ω ω

0 0

As an example of how the dynamic stress error is computed from (5.20), assume
a second-order FLL with a noise bandwidth of 2 Hz and a predetection integration
time of 5 ms. From Table 5.6, for a second-order loop B n =

0.53 ω 0 ,so ω 2 = (2/0.53) 2