User`s guide

Kalman Filtering
9-57
The error covariance before filtering (measurement error) is
MeasErrCov
MeasErrCov =
1.1138
while the error covariance after filtering (estimation error) is only
EstErrCov
EstErrCov =
0.2722
Time-Varying Kalman Filter
The t ime-varying Kalman filter is a gen e ra lization o f the steady-state filter for
time-varying systems or L TI systems w ith nonstationary noise covariance.
Given t he plant state and measurement equations
the time-v arying Kalman filter is g iven by the recursions
Measurement update
Time update
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
n1n+[]Ax
ˆ
nn[]Bu n[]+=
Pn 1n+[]AP n n[]A
T
GQ n[]G
T
+=