Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 518

two conditions: a significant temperature change occurring over the set of n updates
used in (9.29) and the establishment of an upper limit, or threshold, for the statistic.
Such a threshold selection will typically be chosen to represent a 3-sigma condition,
dictating use of a value of nine for testing S t . Simulation study and test experience
will generally be required, however, to achieve the desired response characteristics
from the test. When the threshold is exceeded, the precomputed temperature curve
for this error source can be revised. Such revisions are generally done cautiously:
incorrectly revising the temperature sensitivity curve can adversely affect perfor-
mance for a long time until the erroneous adjustment is detected and removed.
Similar statistics and tests can be generated for each error source for which a prede-
termined temperature compensation exists.
Low-cost sensors may also exhibit significant scale-factor asymmetry (i.e., it
may be advisable to separately model gyro and accelerometer scale factors for posi-
tive and negative rotations and accelerations, respectively). Usually, however, the
component of the scale factor that is common for both directions is dominant, and
the asymmetry can barely be observed in the normal operation of the vehicle.
Given the state vector definition in (9.21), the process noise selection should
consider all sources of error that have been excluded (i.e., scale factor asymmetry,
sensor misalignments, and gyro g-sensitivity, if significant). Of course, the expected
noise floor of each sensor is also included. Since most of the unmodeled effects
behave more like biases than noise, caution must be exercised to select appropriate
levels. As is well known, bias errors do not behave like white noise (e.g., a bias accel-
eration error produces a velocity error that grows linearly or an error variance that
grows quadratically). By contrast, representing a bias acceleration error as white
noise (implied through a process noise representation) produces a velocity error
with a variance that grows linearly.
Consider the misalignment of the roll gyro about the lateral axis of the vehicle as
an illustrative example. This error source is generally expected to be constant,
assuming that the gyro case is rigidly attached to the vehicle and does not experience
significant shock (which could change the sensitive element's alignment within the
case). During a heading maneuver, for example, this error source produces an angu-
lar velocity error in the roll gyro's output:

δϕ =∆ Hm (9.30)

θ

where m θ is the misalignment of the roll gyro about the pitch (or lateral) axis of the
vehicle, measured here in degrees; ∆ H represents the magnitude of the heading

maneuver in radians; and is the resultant roll error in degrees. If the vehicle

makes a u-turn at a stoplight, the heading change will be

δϕ

radians, and let us
assume that the maneuver is completed in 5 seconds. The actual roll error that is
induced, assuming a 1º misalignment, will be slightly more than 3

π

π °. If we select a

process noise variance as in (9.31):

q =∆ H m

22

σ (9.31)

ϕ

σ 2

where H is the sensed

heading change of the gyro in each assumed 1-second propagation step. Use of the
(9.31) representation will increase the roll error variance by less than 2.0 degrees

is the error variance assigned to the misalignment, and ∆