StateOutputEstimator
✖
StateOutputEstimator
constructs an estimator for the StateSpaceModel ssm, with estimator gain matrix 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 allBasic Examples (3)Summary of the most common use cases
The output and state estimator for a continuous-time system:
https://wolfram.com/xid/0d4h3qkvniu6n43a-f7vyog
An estimator of a system with unity estimator gain and a sensor at the second output:
https://wolfram.com/xid/0d4h3qkvniu6n43a-rh1ow8
For a discrete-time system, StateOutputEstimator assembles a discrete‐time estimator:
https://wolfram.com/xid/0d4h3qkvniu6n43a-ilus7r
Scope (8)Survey of the scope of standard use cases
A linear estimator for a system with one measured output and one deterministic input:
https://wolfram.com/xid/0d4h3qkvniu6n43a-funump
Specify that the input is stochastic:
https://wolfram.com/xid/0d4h3qkvniu6n43a-nxt6ir
The estimator for a system in which all the outputs are measured and all inputs are deterministic:
https://wolfram.com/xid/0d4h3qkvniu6n43a-s9ybu4
Only the first output is measured:
https://wolfram.com/xid/0d4h3qkvniu6n43a-o45b7f
The first output is measured and the first input is stochastic:
https://wolfram.com/xid/0d4h3qkvniu6n43a-yoktih
All the outputs are measured and all inputs are stochastic:
https://wolfram.com/xid/0d4h3qkvniu6n43a-eplmfb
An estimator for a descriptor state-space model:
https://wolfram.com/xid/0d4h3qkvniu6n43a-fccspi
An estimator for an AffineStateSpaceModel:
https://wolfram.com/xid/0d4h3qkvniu6n43a-hnln7
Compute a set of gains based on the linearized system:
https://wolfram.com/xid/0d4h3qkvniu6n43a-ycnjh5
https://wolfram.com/xid/0d4h3qkvniu6n43a-bi9fa9
Compute the actual and estimated responses:
https://wolfram.com/xid/0d4h3qkvniu6n43a-d7e0k3
https://wolfram.com/xid/0d4h3qkvniu6n43a-x9s00e
https://wolfram.com/xid/0d4h3qkvniu6n43a-fu8ovr
Options (2)Common values & functionality for each option
Method (2)
By default, the estimator is based on the current measurements:
https://wolfram.com/xid/0d4h3qkvniu6n43a-zrj4hq
https://wolfram.com/xid/0d4h3qkvniu6n43a-3o84yn
https://wolfram.com/xid/0d4h3qkvniu6n43a-m216r6
https://wolfram.com/xid/0d4h3qkvniu6n43a-bg8fy1
For continuous-time systems, the current and prediction estimates are equivalent:
https://wolfram.com/xid/0d4h3qkvniu6n43a-jfmup1
https://wolfram.com/xid/0d4h3qkvniu6n43a-ufjrty
Applications (1)Sample problems that can be solved with this function
An observer for a continuous-time system:
https://wolfram.com/xid/0d4h3qkvniu6n43a-c6n3h2
https://wolfram.com/xid/0d4h3qkvniu6n43a-fq3ifa
https://wolfram.com/xid/0d4h3qkvniu6n43a-1p7g2d
Simulate the system with input -t and from a random initial condition:
https://wolfram.com/xid/0d4h3qkvniu6n43a-fll3ix
https://wolfram.com/xid/0d4h3qkvniu6n43a-cktcfq
https://wolfram.com/xid/0d4h3qkvniu6n43a-wlshbz
Compare each state and its estimate:
https://wolfram.com/xid/0d4h3qkvniu6n43a-m1uto3
https://wolfram.com/xid/0d4h3qkvniu6n43a-vivkqk
https://wolfram.com/xid/0d4h3qkvniu6n43a-r8o4nn
https://wolfram.com/xid/0d4h3qkvniu6n43a-gwbl8n
Properties & Relations (2)Properties of the function, and connections to other functions
StateOutputEstimator estimates the states and outputs of a system:
https://wolfram.com/xid/0d4h3qkvniu6n43a-bvx4g0
https://wolfram.com/xid/0d4h3qkvniu6n43a-9bfjj5
https://wolfram.com/xid/0d4h3qkvniu6n43a-v8sfsb
https://wolfram.com/xid/0d4h3qkvniu6n43a-0a49oi
https://wolfram.com/xid/0d4h3qkvniu6n43a-fcnayn
Construct a Kalman estimator for a discrete-time system:
https://wolfram.com/xid/0d4h3qkvniu6n43a-rufe2k
https://wolfram.com/xid/0d4h3qkvniu6n43a-y57n2l
https://wolfram.com/xid/0d4h3qkvniu6n43a-1a2y4r
Use KalmanEstimator directly:
https://wolfram.com/xid/0d4h3qkvniu6n43a-cnoaf5
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).
Wolfram Research (2010), StateOutputEstimator, Wolfram Language function, https://reference.wolfram.com/language/ref/StateOutputEstimator.html (updated 2014).
CMS
Wolfram Language. 2010. "StateOutputEstimator." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/StateOutputEstimator.html.
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
Wolfram Language. (2010). StateOutputEstimator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StateOutputEstimator.html
BibTeX
@misc{reference.wolfram_2024_stateoutputestimator, author="Wolfram Research", title="{StateOutputEstimator}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/StateOutputEstimator.html}", note=[Accessed: 08-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_stateoutputestimator, organization={Wolfram Research}, title={StateOutputEstimator}, year={2014}, url={https://reference.wolfram.com/language/ref/StateOutputEstimator.html}, note=[Accessed: 08-January-2025
]}