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Chapter 3 / Sensors
_ _
The phase error introduced by these approximations shown in Figure 3-9
must be closely monitored. The normalised frequency in this figure is a
function of the time delay and the input signal frequency (fI).
f
: =
3.2.2.2 Bias, Noise and Scale Factor Errors
3.2-19
f
I
1
⋅ t
SN
TD
Equation 3.2-7
Although it is debatable whether the bias and noise errors should be subject
to scale factor errors, the most complex error form for sensor error
estimation arises when the errors involved are substantial and compounded
as shown in Figure 3-10.
CONSTANT
BIAS (CB)
GM NOISE
1ST ORDER (GM1)
INPUT
RANDOM NOISE (RN)
GM 2ND ORDER (GM2)
1
CONSTANT SF (SC)
ASYMMETRIC
SF (AS)
QUADRATIC
SF (QS)
Figure 3-10 : Bias, Noise and Scale Factor Errors
( t ) : = ϕ ( x ( t ) + )
y ϕ
SF
B
1
OUTPUT
Equation 3.2-8
The bias component comprises separately selectable constant bias, Gaussian
noise, random walk and 2 nd order Markov motion,
ϕ
B
( t ) : = ϕCB
+ ϕRN
+ ϕGM1
+ ϕGM2
Equation 3.2-9
The constant bias is initialised from a Gaussian distribution defined by its
standard deviation (σCB).
ϕ
CB
( SNσ
CB ) ≡ N ( 0 , SNσCB
) t : 0
=
Equation 3.2-10