Graphics Programs Reference
In-Depth Information
IA
z
1
=
0
(9.121)
Substituting Eq. (9.117) into (9.121) and collecting terms yield the following
characteristic function:
f
()
z
3
)
z
2
=
+
(
3α βγ
++
+
(
3 β
2α
+
γ
)
z
(
1 α
)
(9.122)
The
αβγ
becomes a Benedict-Bordner filter when
2βααβ
γ
++
---
=
0
(9.123)
Note that for Eq. (9.123) reduces to Eq. (9.102). For a critically damped
filter the gain coefficients are
γ
=
0
ξ
3
α
=
1
(9.124)
ξ
2
)
2
β
=
1.5 1
(
) 1
(
ξ
)
=
1.5 1
(
ξ
(
1
+
ξ
)
(9.125)
)
3
γ
=
(
1
ξ
(9.126)
Note that heavy smoothing takes place when
ξ
1→ξ
, while
=
0
means that
no smoothing is present.
MATLAB Function Ðghk_tracker.mÑ
The function
Ðghk_tracker.mÑ
implements the steady state
αβγ
filter. It is
given in Listing 9.2 in Section 9.11. The syntax is as follows:
[residual, estimate] = ghk_tracker (X0, smoocof, inp, npts, T, nvar)
where
Symbol
Description
Status
X0
initial state vector
input
smoocof
desired smoothing coefficient
input
inp
array of position measurements
input
npts
number of points in input position
input
T
sampling interval
input
nvar
desired noise variance
input
residual
array of position error (residual)
output
estimate
array of predicted position
output
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