# arxOptions

Option set for `arx`

## 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

## Properties

`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)`

## 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.

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