Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 183

acceleration dynamics and will not be aided by an external navigation system, but
must maintain PLL operation. A third-order loop is selected because it is insensitive
to acceleration stress. To minimize its sensitivity to jerk stress, the noise bandwidth,
B n , is chosen to be the widest possible consistent with stability. Table 5.6 indicates
that B n 18 Hz is safe. This limitation has been determined through extensive

Monte Carlo simulations and is related to the maximum predetection integration
time (which is typically the same as the reciprocal of the carrier loop iteration rate)
plus extremes of noise and dynamic range. If B n

≤

=
22.94455 rad/s. The three multipliers shown in Figure 5.20(c) are computed as fol-
lows:

= 18 Hz, then ω 0 = B n /0.7845

3

ω = 12 079 21

11

, .

0

a
b

ω

2

= . ω

2

= 57910 .

30 0

ω = 2 4 . ω = 55 07 .

30 0

If the carrier loop is updated at a 200-Hz rate, then T = 0.005 second for use in
the digital integrators. This completes the third-order filter parameter design. The
remainder of the loop filter design is the implementation of the digital integrator
accumulators to ensure that they will never overflow (i.e., that they have adequate
dynamic range). The use of floating point arithmetic in modern microprocessors
with built-in floating point hardware greatly simplifies this part of the design pro-
cess. Note that in Figure 5.21(b), the velocity accumulator contains the loop filter
estimate of LOS velocity between the antenna phase center and the SV. This esti-
mate includes a self-adjusting bias component that compensates the carrier tracking
loop for the reference oscillator frequency error (i.e., the time bias rate error that is
in common with all tracking channels). Similarly, the acceleration accumulator con-
tains the loop filter estimate of LOS acceleration that includes a self-adjusting bias
component, which compensates the carrier tracking loop for the time rate of change
of the reference oscillator frequency error. These accumulators should be initialized
to zero just before initial loop closure unless good estimates of the correct values are
known a priori. Also, they should be reset to their bias components (as learned by
the navigation process) or to zero if unknown at the exact instance of injecting
external carrier velocity aiding into the closed loop.
It should be noted that the loop filters described in this section, and in general
any loop filters that are based on an adaptation of analog designs, only achieve the
design noise bandwidth, B n , when the product B n T is very small (well below unity).
As this product increases, the true noise bandwidth tends to be larger than the target
value, and eventually the loop becomes unstable. An alternative loop formulation
described in [8] overcomes some of these limitations. However, instability for
extremely large values of the product B n T is inevitable for any loop filter.

5.6 Measurement Errors and Tracking Thresholds

The GPS measurement errors and tracking thresholds are closely related because the
receiver loses lock when the measurement errors exceed a certain boundary.
Because the code and carrier tracking loops are nonlinear, especially near the