Specifications

kalman
16-111
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 bea state-space modelwithmatrices
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.NotethatP is the solution of
the associated Riccati equation. In discrete time, the syntax
[kest,L,P,M,Z] = kalman(sys,Qn,Rn,Nn)
returns the filter 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 nn
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x nn
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y
v
n
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L
M M
x
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nn 1–
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n
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x
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nn 1–
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v
n
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nn 1–
[]
– Du n
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–
()
+=
innovation
ì            
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y
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; x
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PEenn1–
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enn 1–
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T
()
,
n
∞→
lim= enn 1–
[]
xn
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xnn 1–
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–=
ZEenn
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enn
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T
()
,
n
∞→
lim= enn
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xn
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