Graphics Programs Reference
In-Depth Information
The Kalman filter equations can be deduced from Fig. 9.28. The filtering equa-
tion is
x
nn
(
)
=
x
s
()
x
nn
1
=
(
)
+
K
()
y
()
Gx
n n
[
(
1
)
]
(9.127)
The measurement vector is
y
()
Gx
()
v
()
=
+
(9.128)
where
v
()
is zero mean, white Gaussian noise with covariance
ℜ
c
,
E
y
()
y
t
ℜ
c
=
{
()
}
(9.129)
v
x
s
(
n
+
1
)
G
Σ
u
y
1
Φ
z
+
-
K
Σ
Σ
+
+
x
s
()
1
G
Φ
z
Figure 9.28. Structure of the Kalman filter.
The gain (weight) vector is dynamically computed as
1
)
G
t
)
G
t
K
()
P
nn
1
=
(
[
GP
n n
(
1
+
ℜ
c
]
(9.130)
where the measurement noise matrix
P
represents the predictor covariance
matrix, and is equal to
)
Φ
t
)
x
∗
s
P
n
(
+
1
n
)
=
E
x
s
{
(
n
+
1
()
}
=
Φ
P
nn
(
+
Q
(9.131)
where
Q
is the covariance matrix for the input
u
,
Q
E
u
()
u
t
=
{
()
}
(9.132)
Search WWH ::
Custom Search