# arxOptions

Option set for `arx`

## Syntax

`opt = arxOptions`

opt = arxOptions(Name,Value)

## Description

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.

## Input Arguments

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

`InitialCondition`

— Handling of initial conditions

`'auto'`

(default) | `'zero'`

| `'estimate'`

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.

`Focus`

— Error to be minimized

`'prediction'`

(default) | `'simulation'`

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.

`WeightingFilter`

— Weighting prefilter

`[]`

(default) | vector | matrix | cell array | linear system

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.

`EnforceStability`

— Control whether to enforce stability of model

`false`

(default) | `true`

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`

`EstimateCovariance`

— Option to generate parameter covariance data

`true`

(default) | `false`

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.

`Display`

— Option to display estimation progress

`'off'`

(default) | `'on'`

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.

`InputOffset`

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

`[]`

(default) | vector of positive integers | matrix

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.

`OutputOffset`

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

`[]`

(default) | vector | matrix

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.

`OutputWeight`

— Weight of prediction errors in multi-output estimation

`[]`

(default) | positive semidefinite, symmetric matrix

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.

`Regularization`

— Options for regularized estimation of model parameters

`[]`

(default) | positive semidefinite, symmetric matrix

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.

`Advanced`

— Additional advanced options

structure

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)`

## Output Arguments

`opt`

— Options set for `arx`

`arxOptions`

option set

Option set for `arx`

, returned
as an `arxOptions`

option set.

## Examples

### Create Default Options Set for ARX Estimation

opt = arxOptions;

### 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';

## Version History

**Introduced in R2012a**

### R2018a: Renaming of Estimation and Analysis Options

The names of some estimation and analysis options were changed in R2018a. Prior names still work. For details, see the R2018a release note Renaming of Estimation and Analysis Options.

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