Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 513

error of roughly 3º/second at 20 mph, assuming a 2-m wheel track. Calibration of
this error source by the integration filter is therefore essential and will be discussed
in Section 9.3.3. The effects of wheel sensor pulse count quantization are not a sig-
nificant error contributor to accumulated heading error, as recently demonstrated
[50]. The reason for this is that a quantization error, which can induce a heading
error of one distance quantum divided by the wheel track in one sampling interval,
will tend to correct itself in the following sampling interval. For example, if the left
tire had just missed registering a pulse in the current sum of pulse counts, it will cer-
tainly register that pulse in the next pulse count, and so “catch up” in its measure of
accumulated heading change. In statistical parlance, successive quantization-
induced heading errors are strongly negatively correlated; hence, their summation
approaches zero. However, ABSs will sometimes exhibit a random heading error,
whose 1-sigma level is roughly the size of the pulse quantization and so behaves like
an uncorrelated, quantization error. The error can be attributed to noise in the sen-
sor, which generates the pulses; this seems to be accurate, by design, to the pulse
quantum level. Thus, (9.20), though not representative of the effects of true pulse
quantization, may still be representative of the actual heading error growth; thus, it
is generally recommended for consideration in the design of any real-time Kalman
filter algorithm for conservatism.

σσ
H

= t (9.20)

q

where:

σ H = one-sigma heading error (rad)

q =

quantization level (rad)

Table 9.3, abstracted from [29], assesses the magnitudes of various factors
affecting differential tire size.

9.3.2.5 Barometric Altimeter
As mentioned in Section 9.3.2.3, a barometric altimeter can be used to stabilize an
inertial indication of altitude derived by a vertical accelerometer and a gravity
model. In addition, it can be used to augment a GPS-based altitude, as with a
gyro/odometer, or ABS-based augmentation of GPS. Because of the relative geome-

Table 9.3 Factors Affecting Wheel Scale

Factor
Error Factor Possible Error in Radius

Pressure 1 mm/lbf/in 2

Temperature 1 mm/5ºC

Wear 5 mm

Speed 1 mm

Weight 1 mm/100 kg

Source: [29].