
172 Knowledge Discovery from Data Streams
The Kalman filter estimates the state of the system using a set of recursive
equations. These equations are divided into two groups: time update equations
and measurement update equations. The time update equations are respon-
sible for projecting forward (in time) the current state and error covariance
estimates to obtain the a priori estimates for the next time step.
ˆx
−
k
= Aˆx
k−1
(11.8)
P
−
k
= AP
k−1
A
T
+ Q (11.9)
The measurement update equations are responsible for the feedback, i.e.
for incorporating a new measurement into the a priori estimate to obtain an
improved a posteriori estimate.
K
k
=
P
−
k
H
T
HP
−
k
H
T
+ R
(11.10) ...