User`s guide

kalman
11-110
andgeneratesoptimal“current”outputandstateestimates and
using all available measurements including . The gain matrices and
are derived by solving a discrete Riccati equation. The innovation gain
is used to update the prediction using the new measurement .
Usage [kest,L,P] = kalman(sys,Qn,Rn,Nn) returns a state-space model kest of the
Kalman estimator given the plant model
sys and the noise covariance data Qn,
Rn, Nn (matrices above).sys must be a state-space model with matrices
The resulting estimator
kest has as inputs and (or their
discrete-time counterparts) as outputs. You can omit the last input argument
Nn when .
The function
kalman handles both continuous and discrete problems and
produces a continuous estimator when
sys is continuous, and a discrete
estimator otherwise. In continuous time,
kalman also returns the Kalman gain
L and the steady-state error covariance matrix P.NotethatPis the solution of
the associated Riccati equation. In discrete time, the syntax
[kest,L,P,M,Z] = kalman(sys,Qn,Rn,Nn)
returns the filte r gain and innovations gain , as well as the steady-state
error covariances
Finally, use the syntaxes
[kest,L,P] = kalman(sys,Qn,Rn,Nn,sensors,known)
[kest,L,P,M,Z] = kalman(sys,Qn,Rn,Nn,sensors,known)
y
ˆ
nn
[]
x
ˆ
nn
[]
y
v
n
[]
L
M
M
x
ˆ
nn 1–[]
y
v
n
[]
x
ˆ
nn[]x
ˆ
nn 1–[]My
v
n[] Cx
ˆ
nn 1–[]– Du n[]–


+=
innovation
            
QRN
,,
A
BG
C
DH
,,,
uy
v
;[] y
ˆ
;x
ˆ
[]
N0
=
L
M
PEenn1–[]enn 1–[]
T
(),
n∞→
lim= enn 1–[]xn[] xnn 1–[]–=
ZEenn[]enn[]
T
(),
n∞→
lim= enn[]xn[] xnn[]–=