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BUILT-IN MATHEMATICA SYMBOL
StateOutputEstimator[ssm, l]
constructs an estimator for the StateSpaceModel ssm, with estimator gain matrix l.
StateOutputEstimator[{ssm, sensors}, l]
uses only sensors as the measurements of ssm.
StateOutputEstimator[{ssm, sensors, dinputs}, l]
specifies dinputs as the deterministic inputs of ssm.
Details and Options
- The standard state-space model ssm can be given as StateSpaceModel[{a, b, c, d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
-
continuous-time system 
discrete-time system - The descriptor state-space model ssm can be given as StateSpaceModel[{a, b, c, d, e}] in either continuous-time or discrete-time:
-
continuous-time system 
discrete-time system - The inputs
can include stochastic inputs 
and deterministic inputs 
. - The argument dinputs is a list of integers specifying the positions of
in 
. - The outputs
can include measurements 
and other outputs. - The argument sensors is a list of integers specifying the positions of
in 
. - StateOutputEstimator[ssm, l] is equivalent to StateOutputEstimator[{ssm, All, All}, l].
- The estimator gains l can be computed using EstimatorGains, LQEstimatorGains, or DiscreteLQEstimatorGains.
- StateOutputEstimator[ssm, LQEstimatorGains[ssm, ...], ...] gives a Kalman estimator.
- StateOutputEstimator[ssm, EstimatorGains[ssm, ...], ...] gives a Luenberger estimator.
- StateOutputEstimator supports a Method option. The following explicit settings can be given:
-
"CurrentEstimator" constructs the current estimator "PredictionEstimator" constructs the prediction estimator - The current estimate is based on measurements up to the current instant.
- The prediction estimate is based on measurements up to the previous instant.
- StateOutputEstimator gives an estimator with dynamics
for continuous-time systems. The matrices with subscripts 
and 
are submatrices associated with the deterministic inputs 
and the sensors 
. - The predictor estimator of a discrete-time system has dynamics
. - For discrete-time systems, StateOutputEstimator[..., Method->"CurrentEstimator"] gives an estimator with dynamics
, and the current state estimate 
is obtained from the current measurement 
as 
. - Block diagram for the system with estimator:
- The inputs to the estimator model are the deterministic inputs
and the measurements 
. - The outputs of the estimator model consist of the estimated states
and estimates of the measurements 
.
Examplesopen all
Basic Examples (4)
The output and state estimator for a continuous-time system:
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An estimator of a system with unity estimator gain and a sensor at the second output:
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For a discrete-time system, StateOutputEstimator assembles a discrete-time estimator:
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Construct a reduced-order estimator from known gain and similarity matrices:
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New in 8 | Last modified in 9
