This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# StateOutputEstimator

 StateOutputEstimator constructs an estimator for the StateSpaceModel object ss with estimator gain matrix l. StateOutputEstimatoruses only sensors as the measurements of ss. StateOutputEstimatorspecifies dinputs as the deterministic inputs of ss.
• The state-space model ss can be given as StateSpaceModel, 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 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 .
 "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 .
The output and state estimator for a continuous-time system using estimator gains :
An estimator of a system with unity estimator gain and a sensor at the second output:
For a discrete-time system, StateOutputEstimator assembles a discrete-time estimator:
The output and state estimator for a continuous-time system using estimator gains :
 Out[1]=

An estimator of a system with unity estimator gain and a sensor at the second output:
 Out[1]=

For a discrete-time system, StateOutputEstimator assembles a discrete-time estimator:
 Out[1]=
 Scope   (6)
A linear estimator for a system with one measured output and one deterministic input:
Specify that the input is stochastic:
The estimator for a two-input, two-output 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:
 Options   (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:
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:
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