StateOutputEstimator

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 OptionsDetails 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
  • StateOutputEstimator also accepts nonlinear systems specified by AffineStateSpaceModel and NonlinearStateSpaceModel.
  • For nonlinear systems, the operating values of state and input variables are taken into consideration when constructing the estimator.
  • 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 .

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

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 discretetime estimator:

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Introduced in 2010
(8.0)
| Updated in 2014
(10.0)