Specifications

kalman
16-109
16kalman
Purpose Design continuous- or discrete-time Kalman estimator
Syntax [kest,L,P] = kalman(sys,Qn,Rn,Nn)
[kest,L,P,M,Z] = kalman(sys,Qn,Rn,Nn) % discrete time only
[kest,L,P] = kalman(sys,Qn,Rn,Nn,sensors,known)
Description kalman designs a Kalman state estimator given a state-space model of the
plant and the process and measurement noise covariance data. The Kalman
estimator is the optimal solution to the following continuous or discrete
estimation problems.
Continuous-Time Estimation
Given the continuous plant
with known inputs and process and measurement white noise
satisfying
construct a state estimate that minimizes the steady-state error
covariance
The optimal solution is the Kalman filter with equations
where the filter gain is determined by solving an algebraic Riccati equation.
Thisestimatorusestheknowninputs and the measurements togenerate
x
·
Ax Bu Gw++= (state equation)
y
v
Cx Du Hw v++ += (measurement equation)
uwv
,
Ew
()
Ev
()
0, Eww
T
()
Q ,= Evv
T
()
R= , Ewv
T
()
N===
x
ˆ
t
()
PExx
ˆ
–{}
xx
ˆ
–{}
T
()
t
∞→
lim=
x
ˆ
·
Ax
ˆ
Bu L y
v
Cx
ˆ
–
Du–
()
++=
y
ˆ
x
ˆ
C
I
x
ˆ
D
0
u+=
L
uy
v