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What is state space estimation?
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. The “state space” is the Euclidean space in which the variables on the axes are the state variables.
How do you calculate parameters in statistics?
There are several types of parameter estimates:
- Point estimates are the single, most likely value of a parameter. For example, the point estimate of population mean (the parameter) is the sample mean (the parameter estimate).
- Confidence intervals are a range of values likely to contain the population parameter.
What is state in state space model?
State space model (SSM) refers to a class of probabilistic graphical model (Koller and Friedman, 2009) that describes the probabilistic dependence between the latent state variable and the observed measurement. The state or the measurement can be either continuous or discrete.
What is the process of determining parameter values?
The techniques used for parameter estimation are called estimators. Some estimators are: Probability Plotting: A method of finding parameter values where the data is plotted on special plotting paper and parameters are derived from the visual plot.
How to estimate state-space models with structured parameterization?
If you have independent unknown matrix elements in a linear state-space model structure, then it is easier and quicker to use state-space models with structured parameterizations. For imposing dependencies, or to use more complex forms of parameterization, use the idgrey model and the associated greyest estimator.
How to estimate free model parameters in MATLAB?
Estimate the free model parameters, as described in Estimate State-Space Models at the Command Line This approach differs from estimating models with free and canonical parameterizations, where it is not necessary to specify initial parameter values before the estimation.
How to estimate a model at the command line?
Use ssest to estimate the model, as described in Estimate State-Space Models at the Command Line. The iterative search computes gradients of the prediction errors with respect to the parameters using numerical differentiation. The step size is specified by the nuderst command.
How to construct parameter matrices in structured parameterization?
Construct the parameter matrices and initialize the parameter values using the nominal parameter values. The matrices correspond to continuous-time representation. However, to be consistent with the idss object property name, this example uses A, B, and C instead of F, G, and H.