Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 508

All velocity components (both whole value and error quantities) in (9.16) and
(9.17) should be expressed in consistent units (e.g., meters per second for velocity,
and radians for the heading error). Equations (9.16) and (9.17) can be derived by
simply perturbing the equations for speed and heading expressed in terms of the
velocity components.
An additional source of error in the GPS-determined heading is worthy of men-
tion and can be a significant error, depending upon the antenna placement in the
vehicle. The GPS antenna will generally not be installed close to the center of rota-
tion of the car. As illustrated in Figure 9.28, where the antenna is installed a distance
L from the center of rotation of the vehicle, the GPS receiver will detect the heading
rate multiplied by the distance L as a velocity component orthogonal to the true
velocity of the vehicle. Since GPS (in a nonmultiantenna configuration) can only
derive heading from the determined velocity components, a heading error given by
(9.18) results:

δω HLv = (9.18)

where:

ω is the heading rate of the vehicle, typically represented in radians/second

L is the distance from the center of rotation in meters
v is the vehicle's speed in meters per second
δ H is the resultant heading error in radians

To assess the magnitude of this error source, assume that the GPS antenna is 1m
from the center of rotation, the heading rate is 30º/second, and the vehicle speed is 5
mph. A heading error of more than 10º results, which is generally unacceptable for

v

ω

H = L/v δω

ω L

GPS antenna

Figure 9.28 Effect of antenna placement on GPS heading.