Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 497

• All (six or more) accelerometer systems;
•

Two level axis orthogonal accelerometers;

Single longitudinal axis accelerometer and a vertical gyro;

•

Single lateral axis accelerometer with an interface to the vehicle's odometer;

•

A single vertical gyro with an interface to the vehicle's odometer.

•

Obviously, the last two options do not take full advantage of inertial instrumen-
tation, since they make use of an interface to the vehicle's odometer and so are sensi-
tive to both tire wear and road conditions. To better understand the relative
strengths and weaknesses of the various options, it is helpful to first review the
basics of inertial sensing. An in-depth treatment of inertial sensors and systems is
beyond the scope of this text and can be found in [4].
A common misconception is that an accelerometer directly measures a compo-
nent of acceleration: in fact, the accelerometer senses what is often referred to as
specific force [4], the difference between the component of acceleration along its
input (sensitive) axis and the component of gravity along the same axis. Figure 9.23
illustrates the specific force measurement for an accelerometer mounted along the
lateral axis of an automotive vehicle. Note that it is implicitly assumed that the
input axis of the accelerometer is perfectly aligned with the vehicle's lateral dimen-
sion in the figure, which is not realistic. More generally, the misalignment between
the accelerometer's sensitive axis and the vehicle's lateral axis is a source of error
that must be considered in the design of the navigation system. Neglecting this mis-
alignment in Figure 9.23, the angle

(in radians) represents the roll of the automo-
bile, or the rotation of the vehicle's vertical axis about its longitudinal axis with
respect to the local vertical, b L , the inherent bias of the accelerometer (in m/s 2 ), and
a L , the lateral acceleration component (also in m/s 2 ). Accounting also for a
dimensionless scale factor error s L , the output of the accelerometer can be modeled
(in m/s 2 ) as:

ϕ

( ) ( )

m

a =+ 1 s abg + − sin ϕ ≈+ 1 s abg + − ϕ (9.12)

L LL L LL L

where the indicated approximation is valid for small roll angles, and the m super-
script denotes measured value. A similar equation exists for an accelerometer
mounted along the longitudinal axis of the vehicle, with independent bias and scale
factor errors and with the roll angle replaced by the pitch angle of the vehicle. Equa-
tion (9.12) and Figure 9.23 illustrate the difficulty in directly measuring acceleration.
A similar misconception exists relative to the gyro (i.e., that it simply measures
the rate of rotation of the vehicle in which it is mounted along its sensitive axis).

b

gsin ϕ

Local level

ϕ

Figure 9.23 Error effects upon lateral accelerometer.