Graphics Programs Reference
In-Depth Information
α
β
T
K
=
(9.90)
⁄
G
=
(9.91)
1
0
1
T
01
Φ
=
(9.92)
-
+
x
p
()
x
0
()
Σ
Σ
Σ
1
α
delay,
z
+
+
+
+
x
s
()
ß
s
T
()
β
---
Σ
1
delay,
z
+
+
αβ
Figure 9.20. An implementation of an
tracker.
Finally, using Eqs. (9.89) through (9.92) in Eq. (9.72) yields the steady state
noise covariance matrix,
β 2αβ
(
)
2α
2
3αβ
+
2β
------------------------
σ
2
α 42αβ
T
----------------------------------
C
=
(9.93)
(
)
2β
2
T
2
β 2αβ
(
)
------------------------
--------
T
It follows that the position and velocity VRR ratios are, respectively, given by
2α
2
+
α 42αβ
3αβ
2β
σ
2
(
VRR
)
x
=
C
xx
⁄
=
---------------------------------------
(9.94)
(
)
2β
2
α 42αβ
1
T
2
C
ß
ß
σ
2
-----
----------------------------------
(
VRR
)
ß
=
⁄
=
(9.95)
(
)
The stability of the filter is determined from its system transfer func-
tions. For this purpose, compute the roots for Eq. (9.80) with
αβ
A
from Eq.
(9.89),
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