Specifications

Kalman Filtering
10-57
EstErrCov
EstErrCov =
0.2722
Time-Varying Kalman Filter
The time-varying Kalman filter is a generalization of the steady-state filter for
time-varying systems or LTI systems with nonstationary noise covariance.
Given the plant state and measurement equations
the time-varying Kalman filter is given by the recursions
Measurement update
Time update
with and as defined on page 10-50, and in the following.
xn 1+
[]
Ax n
[]
Bu n
[]
Gw n
[]
++=
y
v
n
[]
Cx n
[]
vn
[]
+=
x
ˆ
nn
[]
x
ˆ
nn 1–
[]
Mn
[]
y
v
n
[]
Cx
ˆ
nn 1–
[]
–
()
+=
Mn
[]
Pnn 1–
[]
C
T
Rn
[]
CP n n 1–
[]
C
T
+
()
1–
=
Pnn
[]
IMn
[]
C–
()
Pnn 1–
[]
=
x
ˆ
n 1 n+
[]
Ax
ˆ
nn
[]
Bu n
[]
+=
Pn 1 n+
[]
AP n n
[]
A
T
GQ n
[]
G
T
+=
x
ˆ
nn 1–
[]
x
ˆ
nn
[]
Qn
[]
Ewn
[]
wn
[]
T
()
=
Rn
[]
Evn
[]
vn
[]
T
()
=
Pnn[]Exn[] xnn[]–{}xn[] xnn[]–{}
T
()=
Pnn 1–[]Exn[] xnn 1–[]–{}xn[] xnn 1–[]–{}
T
()=