# ssregestOptions

Option set for `ssregest`

## Description

## Examples

### Create Default Option Set for State-Space Estimation Using Reduction of Regularized ARX Model

options = ssregestOptions;

### Specify Options for State-Space Estimation Using Reduction of Regularized ARX Model

Create an option set for `ssregest`

that fixes the value of the initial states to `'zero'`

. Also, set the `Display`

to `'on'`

.

opt = ssregestOptions('InitialState','zero','Display','on');

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

.

opt = ssregestOptions; opt.InitialState = 'zero'; opt.Display = 'on';

## 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.*

**Example: **`opt = ssregestOptions('InitialState','zero')`

fixes
the value of the initial states to zero.

`InitialState`

— Handling of initial states

`'estimate'`

(default) | `'zero'`

Handling of initial states during estimation, specified as one of the following values:

`'zero'`

— The initial state is set to zero.`'estimate'`

— The initial state is treated as an independent estimation parameter.

`ARXOrder`

— ARX model orders

`'auto'`

(default) | matrix of nonnegative integers

ARX model orders, specified as a matrix of nonnegative integers ```
[na
nb nk]
```

. The `max(ARXOrder)+1`

must be greater
than the desired state-space model order (number of states). If you
specify a value, it is recommended that you use a large value for `nb`

order.
To learn more about ARX model orders, see `arx`

.

`RegularizationKernel`

— Regularizing kernel

`'TC'`

(default) | `'SE'`

| `'SS'`

| `'HF'`

| `'DI'`

| `'DC'`

Regularizing kernel used for regularized estimates of the underlying ARX model, specified as one of the following values:

`'TC'`

— Tuned and correlated kernel`'SE'`

— Squared exponential kernel`'SS'`

— Stable spline kernel`'HF'`

— High frequency stable spline kernel`'DI'`

— Diagonal kernel`'DC'`

— Diagonal and correlated kernel

For more information, see [1].

`Reduction`

— Options for model order reduction

structure

Options for model order reduction, specified as a structure with the following fields:

`StateElimMethod`

State elimination method. Specifies how to eliminate the weakly coupled states (states with smallest Hankel singular values). Specified as one of the following values:

`'MatchDC'`

Discards the specified states and alters the remaining states to preserve the DC gain. `'Truncate'`

Discards the specified states without altering the remaining states. This method tends to product a better approximation in the frequency domain, but the DC gains are not guaranteed to match. **Default:**`'Truncate'`

`AbsTol, RelTol`

Absolute and relative error tolerance for stable/unstable decomposition. Positive scalar values. For an input model

*G*with unstable poles, the reduction algorithm of`ssregest`

first extracts the stable dynamics by computing the stable/unstable decomposition*G*→*GS*+*GU*. The`AbsTol`

and`RelTol`

tolerances control the accuracy of this decomposition by ensuring that the frequency responses of*G*and*GS*+*GU*differ by no more than`AbsTol`

+`RelTol`

*abs(*G*). Increasing these tolerances helps separate nearby stable and unstable modes at the expense of accuracy. See`stabsep`

(Control System Toolbox) for more information.**Default:**`AbsTol = 0; RelTol = 1e-8`

`Offset`

Offset for the stable/unstable boundary. Positive scalar value. In the stable/unstable decomposition, the stable term includes only poles satisfying

`Re(s) < -Offset * max(1,|Im(s)|)`

(Continuous time)`|z| < 1 - Offset`

(Discrete time)

Increase the value of

`Offset`

to treat poles close to the stability boundary as unstable.**Default:**`1e-8`

`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.

`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.

`InputInterSample`

— Input-channel intersample behavior

`'auto'`

| `'zoh'`

| `'foh'`

| `'bl'`

Input-channel intersample behavior for transformations between discrete time and continuous time, specified as `'auto'`

, `'zoh'`

,`'foh'`

, or `'bl'`

.

The definitions of the three behavior values are as follows:

`'zoh'`

— Zero-order hold maintains a piecewise-constant input signal between samples.`'foh'`

— First-order hold maintains a piecewise-linear input signal between samples.`'bl'`

— Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.

`iddata`

objects have a similar property,
`data.InterSample`

, that contains the same behavior value options.
When the `InputInterSample`

value is `'auto'`

and
the estimation data is in an `iddata`

object `data`

, the
software uses the `data.InterSample`

value. When the estimation data
is instead contained in a timetable or a matrix pair, with the `'auto'`

option, the software uses `'zoh'`

.

The software applies the same option value to all channels and all experiments.

`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.

`Advanced`

— Advanced estimation options

structure

Advanced options for regularized estimation, specified as a structure with the following fields:

`MaxSize`

— Maximum allowable size of Jacobian matrices formed during estimation, specified as a large positive number.**Default:**`250e3`

`SearchMethod`

— Search method for estimating regularization parameters, specified as one of the following values:`'gn'`

: Quasi-Newton line search.`'fmincon'`

: Trust-region-reflective constrained minimizer. In general,`'fmincon'`

is better than`'gn'`

for handling bounds on regularization parameters that are imposed automatically during estimation.

**Default:**`'fmincon'`

## Output Arguments

`options`

— Option set for `ssregest`

`ssregestOptions`

options set

Estimation options for `ssregest`

, returned as an
`ssregestoptions`

option set.

## References

[1] T. Chen, H. Ohlsson, and L. Ljung. “On
the Estimation of Transfer Functions, Regularizations and Gaussian
Processes - Revisited”, *Automatica*,
Volume 48, August 2012.

## Version History

**Introduced in R2014a**

### R2022b: `InputInterSample`

option allows intersample behavior specification for continuous models estimated from timetables or matrices.

`iddata`

objects contain an `InterSample`

property that
describes the behavior of the signal between sample points. The
`InputInterSample`

option implements a version of that property in
`ssregestOptions`

so that intersample behavior can be specified also when
estimation data is stored in timetables or matrices.

### 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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