Estimate State-Space Models in System Identification App

Select Estimate > State Space Models.
The State Space Models dialog box opens.
Tip
For more information on the options in the dialog box, click Help.
Specify a model name by clicking adjacent to Model name. The name of the model must be unique in the Model Board.
Select the Specify value option (if not already selected) and specify the model order in the edit field. Model order refers to the number of states in the state-space model.
Tip
When you do not know the model order, search for and select an order. For more information, see Estimate Model With Selected Order in the App.
Select the Continuous-time or Discrete-time option to specify the type of model to estimate.
You cannot estimate a discrete-time model if the working data is continuous-time frequency-domain data.
Expand the Model Structure Configuration section to select the model structure, such as canonical form, whether to estimate the disturbance component (K matrix) and specification of feedthrough and input delays.
For more information about the type of state-space parameterization, see Supported State-Space Parameterizations.
Expand the Estimation Options section to select the estimation method and configure the cost function.
Select one of the following Estimation Method from the drop-down list and configure the options. For more information about these methods, see State-Space Model Estimation Methods.
Subspace (N4SID)
1. In the N4Weight drop-down list, specify the weighting scheme used for singular-value decomposition by the N4SID algorithm.
  The N4SID algorithm is used both by the subspace and Prediction Error Minimization (PEM) methods.
2. In the N4Horizon field, specify the forward and backward prediction horizons used by the N4SID algorithm.
  The N4SID algorithm is used both by the subspace and PEM methods.
3. In the Focus drop-down list, select how to weigh the relative importance of the fit at different frequencies. For more information about each option, see Assigning Estimation Weightings.
4. Select the Allow unstable models check box to specify whether to allow the estimation process to use parameter values that may lead to unstable models.
  Setting this option is same as setting the estimation option Focus to 'prediction' at the command line. An unstable model is delivered only if it produces a better fit to the data than other stable models computed during the estimation process.
5. Select the Estimate covariance check box if you want the algorithm to compute parameter uncertainties.
  Effects of such uncertainties are displayed on plots as model confidence regions. Skipping uncertainty computation reduces computation time for complex models and large data sets.
6. Select the Display progress check box to open a progress viewer window during estimation.
7. In the Initial state list, specify how you want the algorithm to treat initial states. For more information about the available options, see Specifying Initial States for Iterative Estimation Algorithms.
Prediction Error Minimization (PEM)
- In the N4Weight drop-down list, specify the weighting scheme used for singular-value decomposition by the N4SID algorithm.
  The N4SID algorithm is used both by the subspace and Prediction Error Minimization (PEM) methods.
- In the N4Horizon field, specify the forward and backward prediction horizons used by the N4SID algorithm.
  The N4SID algorithm is used both by the subspace and PEM methods.
- In the Focus drop-down list, select how to weigh the relative importance of the fit at different frequencies. For more information about each option, see Assigning Estimation Weightings.
- Select the Allow unstable models check box to specify whether to allow the estimation process to use parameter values that may lead to unstable models.
  Setting this option is same as setting the estimation option Focus to 'prediction' at the command line. An unstable model is delivered only if it produces a better fit to the data than other stable models computed during the estimation process.
- Select the Estimate covariance check box if you want the algorithm to compute parameter uncertainties.
  Effects of such uncertainties are displayed on plots as model confidence regions. Skipping uncertainty computation reduces computation time for complex models and large data sets.
- Select the Display progress check box to open a progress viewer window during estimation.
- In the Initial state list, specify how you want the algorithm to treat initial states. For more information about the available options, see Specifying Initial States for Iterative Estimation Algorithms.
  Tip
  If you get an inaccurate fit, try setting a specific method for handling initial states rather than choosing it automatically.
- Click Regularization to obtain regularized estimates of model parameters. Specify the regularization constants in the Regularization Options dialog box. To learn more, see Regularized Estimates of Model Parameters.
- Click Iteration Options to specify options for controlling the iterations. The Options for Iterative Minimization dialog box opens.
  Iteration Options
  In the Options for Iterative Minimization dialog box, you can specify the following iteration options:
  Search Method — Method used by the iterative search algorithm. Search method is auto by default. The descent direction is calculated using gn (Gauss-Newton), gna (Adaptive Gauss-Newton), lm (Levenberg-Marquardt), lsqnonlin (Trust-Region Reflective Newton), and grad (Gradient Search) successively at each iteration until a sufficient reduction in error is achieved.
  Output weighting — Weighting applied to the loss function to be minimized. Use this option for multi-output estimations only. Specify as 'noise' or a positive semidefinite matrix of size equal the number of outputs.
  Maximum number of iterations — Maximum number of iterations to use during search.
  Termination tolerance — Tolerance value when the iterations should terminate.
  Error threshold for outlier penalty — Robustification of the quadratic criterion of fit.
Regularized Reduction
- In the Regularization Kernel drop-down list, select the regularizing kernel to use for regularized estimation of the underlying ARX model. To learn more, see Regularized Estimates of Model Parameters.
- In the ARX Orders field, specify the order of the underlying ARX model. By default, the orders are automatically computed by the estimation algorithm. If you specify a value, it is recommended that you use a large value for nb order. To learn more about ARX orders, see arx.
- In the Focus drop-down list, select how to weigh the relative importance of the fit at different frequencies. For more information about each option, see Assigning Estimation Weightings.
- In the Reduction Method drop-down list, specify the reduction method:
  Truncate — Discards the specified states without altering the remaining states. This method tends to product a better approximation in the frequency domain, but the DC gains are not guaranteed to match.
  MatchDC — Discards the specified states and alters the remaining states to preserve the DC gain.
- Select the Estimate covariance check box if you want the algorithm to compute parameter uncertainties.
  Effects of such uncertainties are displayed on plots as model confidence regions. Skipping uncertainty computation reduces computation time for complex models and large data sets.
- Select the Display progress check box to open a progress viewer window during estimation.
- In the Initial state list, specify how you want the algorithm to treat initial states. For more information about the available options, see Specifying Initial States for Iterative Estimation Algorithms.
  Tip
  If you get an inaccurate fit, try setting a specific method for handling initial states rather than choosing it automatically.
The estimation process uses parameter values that always lead to a stable model.
Click Estimate to estimate the model. A new model gets added to the System Identification app.

Assigning Estimation Weightings

You can specify how the estimation algorithm weights the fit at various frequencies. In the app, set Focus to one of the following options:

Prediction — Uses the inverse of the noise model H to weigh the relative importance of how closely to fit the data in various frequency ranges. Corresponds to minimizing one-step-ahead prediction, which typically favors the fit over a short time interval. Optimized for output prediction applications.
Simulation — Uses the input spectrum to weigh the relative importance of the fit in a specific frequency range. Does not use the noise model to weigh the relative importance of how closely to fit the data in various frequency ranges. Optimized for output simulation applications.
Stability — Estimates the best stable model. For more information about model stability, see Unstable Models.
Filter — Specify a custom filter to open the Estimation Focus dialog box, where you can enter a filter, as described in Simple Passband Filter or Defining a Custom Filter. This prefiltering applies only for estimating the dynamics from input to output. The disturbance model is determined from the estimation data.

Documentation

Estimate State-Space Models in System Identification App

Assigning Estimation Weightings

System Identification Toolbox Documentation

Support