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arxOptions

Option set for arx

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Description

Use an arxOptions object to specify options for estimating parameters of ARX, ARIX, AR, or ARI models through the arx function. You can specify options such as the handling of initial conditions or the ability to display estimation progress.

Creation

Syntax

opt = arxOptions
opt = arxOptions(Name,Value)

Description

example

opt = arxOptions creates the default options set for arx.

example

opt = arxOptions(Name,Value) creates an option set with the options specified by one or more Name,Value pair arguments.

Properties

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Handling of initial conditions during estimation using frequency-domain data, specified as the comma-separated pair consisting of 'InitialCondition' and one of the following values:

  • 'zero' — The initial conditions are set to zero.

  • 'estimate' — The initial conditions are treated as independent estimation parameters.

  • 'auto' — The software chooses the method to handle initial conditions based on the estimation data.

Error to be minimized in the loss function during estimation, specified as the comma-separated pair consisting of 'Focus' and one of the following values:

  • 'prediction' — The one-step ahead prediction error between measured and predicted outputs is minimized during estimation. As a result, the estimation focuses on producing a good predictor model.

  • 'simulation' — The simulation error between measured and simulated outputs is minimized during estimation. As a result, the estimation focuses on making a good fit for simulation of model response with the current inputs.

The Focus option can be interpreted as a weighting filter in the loss function. For more information, see Loss Function and Model Quality Metrics.

Weighting prefilter applied to the loss function to be minimized during estimation. To understand the effect of WeightingFilter on the loss function, see Loss Function and Model Quality Metrics.

Specify WeightingFilter as one of the following values:

  • [] — No weighting prefilter is used.

  • Passbands — Specify a row vector or matrix containing frequency values that define desired passbands. You select a frequency band where the fit between estimated model and estimation data is optimized. For example, [wl,wh] where wl and wh represent lower and upper limits of a passband. For a matrix with several rows defining frequency passbands, [w1l,w1h;w2l,w2h;w3l,w3h;...], the estimation algorithm uses the union of the frequency ranges to define the estimation passband.

    Passbands are expressed in rad/TimeUnit for time-domain data and in FrequencyUnit for frequency-domain data, where TimeUnit and FrequencyUnit are the time and frequency units of the estimation data.

  • SISO filter — Specify a single-input-single-output (SISO) linear filter in one of the following ways:

    • A SISO LTI model

    • {A,B,C,D} format, which specifies the state-space matrices of a filter with the same sample time as estimation data.

    • {numerator,denominator} format, which specifies the numerator and denominator of the filter as a transfer function with same sample time as estimation data.

      This option calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function.

  • Weighting vector — Applicable for frequency-domain data only. Specify a column vector of weights. This vector must have the same length as the frequency vector of the data set, Data.Frequency. Each input and output response in the data is multiplied by the corresponding weight at that frequency.

Control whether to enforce stability of estimated model, specified as the comma-separated pair consisting of 'EnforceStability' and either true or false.

This option is not available for multi-output models with a non-diagonal A polynomial array.

Data Types: logical

Option to generate parameter covariance data, specified as true or false.

If EstimateCovariance is true, then use getcov to fetch the covariance matrix from the estimated model.

Option to display the estimation progress, specified as one of the following values:

  • 'on' — Information on model structure and estimation results are displayed in a progress-viewer window.

  • 'off' — No progress or results information is displayed.

Removal of offset from time-domain input data during estimation, specified as one of the following:

  • A column vector of positive integers of length Nu, where Nu is the number of inputs.

  • [] — Indicates no offset.

  • Nu-by-Ne matrix — For multi-experiment data, specify InputOffset as an Nu-by-Ne matrix. Nu is the number of inputs and Ne is the number of experiments.

Each entry specified by InputOffset is subtracted from the corresponding input data.

Removal of offset from time-domain output data during estimation, specified as one of the following:

  • A column vector of length Ny, where Ny is the number of outputs.

  • [] — Indicates no offset.

  • Ny-by-Ne matrix — For multi-experiment data, specify OutputOffset as a Ny-by-Ne matrix. Ny is the number of outputs, and Ne is the number of experiments.

Each entry specified by OutputOffset is subtracted from the corresponding output data.

Weight of prediction errors in multi-output estimation, specified as one of the following values:

  • Positive semidefinite, symmetric matrix (W). The software minimizes the trace of the weighted prediction error matrix trace(E'*E*W/N) where:

    • E is the matrix of prediction errors, with one column for each output, and W is the positive semidefinite, symmetric matrix of size equal to the number of outputs. Use W to specify the relative importance of outputs in multiple-output models, or the reliability of corresponding data.

    • N is the number of data samples.

  • [] — No weighting is used. Specifying as [] is the same as eye(Ny), where Ny is the number of outputs.

This option is relevant only for multi-output models.

Options for regularized estimation of model parameters, specified as a structure with the following fields:

  • Lambda — Constant that determines the bias versus variance tradeoff.

    Specify a positive scalar to add the regularization term to the estimation cost.

    The default value of zero implies no regularization.

    Default: 0

  • R — Weighting matrix.

    Specify a positive scalar or a positive definite matrix. The length of the matrix must be equal to the number of free parameters (np) of the model. For ARX model, np = sum(sum([na nb]).

    Default: 1

  • Nominal — This option is not used for ARX models.

    Default: 0

Use arxRegul to automatically determine Lambda and R values.

For more information on regularization, see Regularized Estimates of Model Parameters.

Additional advanced options, specified as a structure with the following fields:

  • MaxSize — Specifies the maximum number of elements in a segment when input-output data is split into segments.

    MaxSize must be a positive integer.

    Default: 250000

  • StabilityThreshold — Specifies thresholds for stability tests.

    StabilityThreshold is a structure with the following fields:

    • s — Specifies the location of the right-most pole to test the stability of continuous-time models. A model is considered stable when its right-most pole is to the left of s.

      Default: 0

    • z — Specifies the maximum distance of all poles from the origin to test stability of discrete-time models. A model is considered stable if all poles are within the distance z from the origin.

      Default: 1+sqrt(eps)

Examples

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Open Live Script
opt = arxOptions;
Open Live Script

Create an options set for arx using zero initial conditions for estimation. Set Display to 'on'. 

opt = arxOptions('InitialCondition','zero','Display','on');

Alternatively, use dot notation to set the values of opt. 

opt = arxOptions;
opt.InitialCondition = 'zero';
opt.Display = 'on';

Version History

Introduced in R2012a

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See Also

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