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Chapter 3 / Sensors
_ _
( t ) : = ϕ ( N ( 0 , σ ) , 1,
)
y ω
D 2L
3.2-22
SN
GM2
SN
GM2
Equation 3.2-24
The SIMULINK conversion from the continuous to the discrete domain,
c2dm
[ SN _ NP , SN _ DP ]
: =
2
[ 1,
2 ⋅ ω ω ] ⎟
⎞
SN GM1
, SN GM2
, SN R
⎠
⎜
⎛ 2
SN ωGM2
,
ω
⎝
SN_R2NP(z)
SN_R2DP(z)
1/SN_SF
1-z-1
0
SN_B_7
Equation 3.2-25
Figure 3-12 : 2 nd Order Gauss-Markov Motion
The scale factor error is a combination of separately selectable constant,
quadratic and asymmetric terms,
ϕ
SF
( x ) : = ϕ ( x , σ ) + ϕ ( x , σ ) + ϕ ( x , σ )
CS
SN
CS
QS
SN
QS
AS
1
SN
AS
Equation 3.2-26
The scale factor coefficients are initialised using Gaussian distributions
defined by appropriate standard deviations,
x ⋅ N
( x )
( 0 , σ ) + ⋅ ⎜⎛
⋅ ( σ ) + ( σ ) ⎟⎞ SN CS x x N 0 ,
= SN QS N 0 ,
t : 0
t : = 0
SN AS t : = 0 ⎠
3.2.2.3 Analogue to Digital Conversion
⎝
ϕ
SF
: =
Equation 3.2-27
The reference input, dynamics and error models are processed at a
frequency representative of their analogue equivalent. The error models
arising from the conversion of the analogue measurements into digital form
are shown in Figure 3-13 and comprise:
• Anti-Aliasing filter ( bit 23 )
• Range limiting (without word length wrapping) ( bit 24 )
• Quantisation ( bit 25 )
• Uniformly distributed “N” bit ADC noise ( bit 26 )