Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 512

∆ H

d = Right wheel
distance traveled

R

d = Left wheel
distance traveled

L

T = Wheel track

∆ H=(d -d)/T
R

L

Figure 9.31 Heading change determination using rear wheels.

where d R and d L are the distances traveled by the right and left wheels, respectively,
and T is the wheel track (the distance between the tires).
In (9.19), the right and left wheel distances are generally represented in meters,
as is the wheel track, resulting in the computed heading change H in radians. Note

that (9.19) is valid only when the sensors are installed on the rear wheels. When the
front wheels are used, the geometry changes, since the front wheels develop wheel
angles, denoted

∆

in Figure 9.32.
Because of the wheel angles, the original wheel track, T , is no longer perpendicu-
lar to the tires, and the effective wheel track, denoted

γ

T in Figure 9.32, is reduced by ′

cos . This shortening of the wheel track becomes more significant as the wheel

angle increases (i.e., the heading rate is more rapid). Ignoring this effect for front
wheel installations can induce significant heading errors in turns. Since the wheel
angles are generally not known to the DR system, an approximate method for com-
puting the effective track width is required. Several such methods are described in
[49]. The track width variation with vehicle speed is also referenced in [49].
Heading determination via differential odometry is susceptible to gross errors
when the pulse count difference is induced by either tire slipping or skidding, as dis-
cussed for the transmission odometer, but also when there is significant differential
tire pressure. A relatively small difference in tire pressure, if not calibrated, can lead
to significant error growth: a difference in tire size of 1% produces a heading rate

γ

∆ H

d = Right wheel
distance traveled

R

d = Left wheel
distance traveled

L

T' = Adjusted wheel track

γ = Wheel angle γ

T = Wheel track

T' = T cos
H=(d -d)/T'

γ

R L

Figure 9.32 Heading change determination using front wheels.