Option set for `arx`

`opt = arxOptions`

opt = arxOptions(Name,Value)

creates
the default options set for `opt`

= arxOptions`arx`

.

creates
an option set with the options specified by one or more `opt`

= arxOptions(`Name,Value`

)`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'`

| `'stability'`

| vector | matrix | linear systemEstimation focus that defines how the errors *e* between
the measured and the modeled outputs are weighed at specific frequencies
during the minimization of the prediction error, specified as one
of the following values:

`'prediction'`

— Automatically calculates the weighting function as a product of the input spectrum and the inverse of the noise spectrum. The weighting function minimizes the one-step-ahead prediction. This approach 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.This option focuses on producing a good predictor and does not enforce model stability. Use

`'stability'`

when you want to ensure a stable model.`'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. This method provides 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 lower and upper 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.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 SISO linear filter in one of the following ways:

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

`{A,B,C,D}`

format, which specifies the state-space matrices of the filter`{numerator, denominator}`

format, which specifies the numerator and denominator of the filter transfer functionThis 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, 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.

`'EstCovar'`

— Control whether to generate parameter covariance data`true`

(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:

`'on'`

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

— No progress or results information is displayed.

`'InputOffset'`

— Removal of offset from time-domain input data during estimation`[]`

(default) | vector of positive integers | matrixRemoval of offset from time-domain input data during estimation,
specified as the comma-separated pair consisting of `'InputOffset'`

and
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.

`'OutputOffset'`

— Removal of offset from time-domain output data during estimation`[]`

(default) | vector | matrixRemoval of offset from time-domain output data during estimation,
specified as the comma-separated pair consisting of `'OutputOffset'`

and
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.

`'OutputWeight'`

— Weight of prediction errors in multi-output estimation`[]`

(default) | positive semidefinite, symmetric matrixWeight 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-input, multiple-output models, or the reliability of corresponding data.`N`

is the number of data samples.

This option is relevant only for multi-output models.

`[]`

— No weighting is used. Specifying as`[]`

is the same as`eye(Ny)`

, where`Ny`

is the number of outputs.

`'Regularization'`

— Options for regularized estimation of model parameters`[]`

(default) | positive semidefinite, symmetric matrixOptions 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`

— 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.

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

`'Advanced'`

— Additional advanced optionsstructureAdditional 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)`

`opt`

— Options set for `arx`

`arxOptions`

option setOption set for `arx`

, returned
as an `arxOptions`

option set.

opt = arxOptions;

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';

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