Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 184

threshold regions, only Monte Carlo simulations of the GPS receiver under the com-
bined dynamic and SNR conditions will determine the true tracking performance
[9]. However, general rules that approximate the measurement errors of the track-
ing loops can be used based on closed form equations. Numerous sources of mea-
surement errors are in each type of tracking loop. However, it is sufficient for
rule-of-thumb tracking thresholds to analyze only the dominant error sources.

5.6.1 PLL Tracking Loop Measurement Errors
The dominant sources of phase error in a GPS receiver PLL are phase jitter and dynamic
stress error. A conservative rule of thumb for tracking threshold is that the 3-sigma jitter
must not exceed one-fourth of the phase pull-in range of the PLL discriminator. Only
arctangent carrier phase discriminators are considered for the generic receiver design. In
the case of a dataless PLL four-quadrant arctangent discriminator whose phase pull-in
range is 360º, the 3-sigma rule threshold is therefore 90º. For the case where there is data
modulation, the PLL two-quadrant arctangent discriminator must be used and has a
phase pull-in range of 180º. Therefore the 3-sigma rule threshold is 45º. Therefore, the
PLL rule thresholds are stated as follows:

3 σ =+≤°

=+≤°

3 σ θ 90 (dataless)

(data present)

PLL j e

(5.4)

3 σ 3 σ θ 45

PLL j e

where:

σ j = 1-sigma phase jitter from all sources except dynamic stress error

θ e = dynamic stress error in the PLL tracking loop

Equation (5.4) implies that dynamic stress error is a 3-sigma effect and is addi-
tive to the phase jitter. The phase jitter is the RSS of every source of uncorrelated
phase error, such as thermal noise and oscillator noise. Oscillator noise includes
vibration-induced jitter and Allan deviation-induced jitter. It also includes satellite
oscillator phase noise. Even though IS-GPS-200 [2] specifies that this is no greater
than 0.1 rad (5.7º) 1-sigma tracking error in a 10-Hz PLL, the operational SVs
exhibit about an order of magnitude lower error than this to date. This external
source of noise jitter is not included in the foregoing analysis but should be consid-
ered in very narrowband PLL applications.
In the P(Y) code and C/A code examples to follow, the presence of data modula-
tion is assumed. Expanding on (5.4), the 1-sigma rule threshold for the PLL tracking
loop for the two-quadrant arctangent discriminator is therefore:

θ

2 2 2 e

(5.5)

σ = σ + σ + θ + ≤ 15 ° (data present)

PLL tPLL v A

3

where:

σ tPLL = 1-sigma thermal noise in degrees

σ v = 1-sigma vibration-induced oscillator jitter in degrees