Contents

arxOptions

Option set for ar

Syntax

opt = arxOptions
opt = arxOptions(Name,Value)

Description

opt = arxOptions creates the default options set for arx.

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

Input Arguments

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Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'InitialCondition' — Initial condition'auto' (default) | 'zero' | 'estimate' | 'backcast'

Specify how initial conditions are handled during estimation.

InitialCondition requires one of the following values:

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

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

  • 'backcast' — The initial conditions are estimated using the best least squares fit.

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

'Focus' — Estimation focus'prediction' (default) | 'simulation' | vector | matrix | linear system

Defines how the errors e between the measured and the modeled outputs are weighed at specific frequencies during the minimization of the prediction error.

Higher weighting at specific frequencies emphasizes the requirement for a good fit at these frequencies.

Focus requires one of the following values:

  • 'simulation' — Estimates the model using the frequency weighting of the transfer function that is given by the input spectrum. Typically, this method favors the frequency range where the input spectrum has the most power.

  • 'prediction' — Automatically calculates the weighting function as a product of the input spectrum and the inverse of the noise model. The weighting function minimizes one-step-ahead prediction, which typically favors fitting small time intervals (higher frequency range). From a statistical-variance point of view, this weighting function is optimal. However, this method neglects the approximation aspects (bias) of the fit. Use 'stability'when you want to ensure a stable model.

  • 'stability' — Same as 'prediction', but with model stability enforced.

  • Passbands — Row vector or matrix containing frequency values that define desired passbands. For example:

    [wl,wh]
    [w1l,w1h;w2l,w2h;w3l,w3h;...]

    where wl and wh represent upper and lower limits of a passband. For a matrix with several rows defining frequency passbands, the algorithm uses union of frequency ranges to define the estimation passband.

  • SISO filter — Enter any SISO linear filter in any of the following ways:

    • A single-input-single-output (SISO) linear system.

    • The {A,B,C,D} format, which specifies the state-space matrices of the filter.

    • The {numerator, denominator} format, which specifies the numerator and denominator of the filter transfer function

      This option calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function. To obtain a good model fit for a specific frequency range, you must choose the filter with a passband in this range. The estimation result is the same if you first prefilter the data using idfilt.

  • Weighting vector — For frequency-domain data only, enter a column vector of weights for 'Focus'. This vector must have the same size as length of 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.

'EstCovar' — Control whether to generate parameter covariance datatrue (default) | false

Controls whether parameter covariance data is generated, specified as true or false.

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

'Display' — Specify whether to display the estimation progress'off' (default) | 'on'

Specify whether to display the estimation progress, specified as one of the following strings:

Display requires one of the following strings:

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

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

'InputOffset' — Remove offset from time-domain input data during estimation[] (default) | vector of positive integers

Removes offset from time-domain input data during estimation, specified as a vector of positive integers.

Specify as a column vector of length Nu, where Nu is the number of inputs.

Use [] to indicate no offset.

For multiexperiment data, specify InputOffset as a 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.

'OutputOffset' — Remove offset from time-domain output data during estimation[] (default) | vector

Removes offset from time domain output data during estimation, specified as a vector of positive integers or [].

Specify as a column vector of length Ny, where Ny is the number of outputs.

Use [] to indicate no offset.

For multiexperiment 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.

'OutputWeight'

Weight of prediction errors in multi-output estimation.

Specify OutputWeight as a positive semidefinite, symmetric matrix (W). The software minimizes the trace of the weighted prediction error matrix trace(E'*E*W). 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-input, multiple-output models, or the reliability of corresponding data.

This option is relevant only for multi-output models.

'Regularization'

Options for regularized estimation of ARX model parameters. For more information on regularization, see Regularized Estimates of Model Parameters.

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 — The nominal value towards which the free parameters are pulled during estimation.

    The default value of zero implies that the parameter values are pulled towards zero. If you are refining a model, you can set the value to 'model' to pull the parameters towards the parameter values of the initial model. The initial parameter values must be finite for this setting to work.

    Default: 0

Use arxRegul to automatically determine Lambda and R values.

'Advanced'

Advanced is 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)

Output Arguments

opt

Option set containing the specified options for arx.

Examples

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Specify Options for ARX Estimation

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';

See Also

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