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 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 prediction 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 .
  • For discrete-time systems, the prediction gain and the current gain have the relationship .
  • 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 .

Examples

open allclose all

Basic Examples  (3)

The output and state estimator for a continuous-time system:

An estimator of a system with unity estimator gain and a sensor at the second output:

For a discrete-time system, StateOutputEstimator assembles a discretetime estimator:

Scope  (8)

A linear estimator for a system with one measured output and one deterministic input:

Specify that the input is stochastic:

The estimator for a system in which all the outputs are measured and all inputs are deterministic:

Only the first output is measured:

The first output is measured and the first input is stochastic:

All the outputs are measured and all inputs are stochastic:

An estimator for a descriptor state-space model:

An estimator for an AffineStateSpaceModel:

Compute a set of gains based on the linearized system:

Construct the estimator:

Compute the actual and estimated responses:

Plot the responses:

Options  (2)

Method  (2)

By default, the estimator is based on the current measurements:

The prediction estimator:

For continuous-time systems, the current and prediction estimates are equivalent:

Applications  (1)

An observer for a continuous-time system:

Simulate the system with input -t and from a random initial condition:

Compare each state and its estimate:

Compare the outputs:

Properties & Relations  (2)

StateOutputEstimator estimates the states and outputs of a system:

Extract the state estimator:

The output estimator:

Construct a Kalman estimator for a discrete-time system:

Use KalmanEstimator directly:

Wolfram Research (2010), StateOutputEstimator, Wolfram Language function, https://reference.wolfram.com/language/ref/StateOutputEstimator.html (updated 2014).

Text

Wolfram Research (2010), StateOutputEstimator, Wolfram Language function, https://reference.wolfram.com/language/ref/StateOutputEstimator.html (updated 2014).

BibTeX

@misc{reference.wolfram_2021_stateoutputestimator, author="Wolfram Research", title="{StateOutputEstimator}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/StateOutputEstimator.html}", note=[Accessed: 16-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_stateoutputestimator, organization={Wolfram Research}, title={StateOutputEstimator}, year={2014}, url={https://reference.wolfram.com/language/ref/StateOutputEstimator.html}, note=[Accessed: 16-October-2021 ]}

CMS

Wolfram Language. 2010. "StateOutputEstimator." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/StateOutputEstimator.html.

APA

Wolfram Language. (2010). StateOutputEstimator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StateOutputEstimator.html