
Single channel signal 33
x
0
,P
0
Predict :
ˆx
−
k
= Aˆx
k−1
+ Bu
k
P
−
k
= AP
k−1
A
T
+ Q
))
Update:
K
k
= P
−
k
M
T
MP
−
k
M
T
+ R
−1
ˆx
k
= ˆx
−
k
+ K
k
(z
k
−Mˆx
−
k
)
P
k
=(I −K
k
M)P
−
k
ff
FIGURE 2.3: The computation of successive system states with Kalman filter.
Kalman filter may be found in [Welch et al., 1960].
MATLAB toolbox by Kevin Murphy avaliable at
http://people.cs.ubc.ca/
˜
murphyk/Software/Kalman/kalman.html
provides Kalman filter formalism for
filtering, smoothing, and parameter estimation for linear dynamical systems.
Many real dynamical systems do not exactly fit the model assumed by Kalman
filter design. The not-modeled dynamics contributes to the component w
k
in equation
2.19. In practice ...