# n4sidOptions

Option set for `n4sid`

## Syntax

`opt = n4sidOptions`

opt = n4sidOptions(Name,Value)

## Description

creates
the default options set for `opt`

= n4sidOptions`n4sid`

.

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

= n4sidOptions(`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.*

`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.

`N4Weight`

— Weighting scheme used for singular-value decomposition by the `N4SID`

algorithm

`'auto'`

(default) | `'MOESP'`

| `'CVA'`

| `'SSARX'`

Weighting scheme used for singular-value decomposition by the N4SID algorithm, specified as one of the following values:

`'MOESP'`

— Uses the MOESP algorithm by Verhaegen [2].`'CVA'`

— Uses the Canonical Variate Algorithm by Larimore [1].Estimation using frequency-domain data always uses

`'CVA'`

.`'SSARX'`

— A subspace identification method that uses an ARX estimation based algorithm to compute the weighting.Specifying this option allows unbiased estimates when using data that is collected in closed-loop operation. For more information about the algorithm, see [4].

`'auto'`

— The estimating function chooses between the`MOESP`

,`CVA`

and`SSARX`

algorithms.

`N4Horizon`

— Forward- and backward-prediction horizons used by the `N4SID`

algorithm

`'auto'`

(default) | vector `[r sy su]`

| `k`

-by-3 matrix

Forward- and backward-prediction horizons used by the N4SID algorithm, specified as one of the following values:

A row vector with three elements —

`[r sy su]`

, where`r`

is the maximum forward prediction horizon, using up to`r`

step-ahead predictors.`sy`

is the number of past outputs, and`su`

is the number of past inputs that are used for the predictions. See pages 209 and 210 in [3] for more information. These numbers can have a substantial influence on the quality of the resulting model, and there are no simple rules for choosing them. Making`'N4Horizon'`

a`k`

-by-3 matrix means that each row of`'N4Horizon'`

is tried, and the value that gives the best (prediction) fit to data is selected.`k`

is the number of guesses of`[r sy su]`

combinations. If you specify N4Horizon as a single column,`r = sy = su`

is used.`'auto'`

— The software uses an Akaike Information Criterion (AIC) for the selection of`sy`

and`su`

.

`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`

.

`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`

— Weighting of prediction errors in multi-output estimations

`[]`

(default) | `'noise'`

| positive semidefinite symmetric matrix

Weighting of prediction errors in multi-output estimations, specified as one of the following values:

`'noise'`

— Minimize $$\mathrm{det}(E\text{'}*E/N)$$, where*E*represents the prediction error and`N`

is the number of data samples. This choice is optimal in a statistical sense and leads to the maximum likelihood estimates in case no data is available about the variance of the noise. This option uses the inverse of the estimated noise variance as the weighting function.Positive semidefinite symmetric matrix (

`W`

) — Minimize 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.`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.

`[]`

— The software chooses between the`'noise'`

or using the identity matrix for`W`

.

This option is relevant only for multi-output models.

`Advanced`

— Additional advanced options

structure

Additional advanced options, specified as a structure with the
field `MaxSize`

. `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

## Output Arguments

`opt`

— Option set for `n4sid`

`n4sidOptions`

option set

Option set for `n4sid`

,
returned as an `n4sidOptions`

option set.

## Examples

### Create Default Options Set for State-Space Estimation Using Subspace Method

opt = n4sidOptions;

### Specify Options for State-Space Estimation Using Subspace Method

Create an options set for `n4sid`

using the `'zero'`

option to initialize the state. Set the `Display`

to `'on'`

.

opt = n4sidOptions('InitialState','zero','Display','on');

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

.

opt = n4sidOptions; opt.InitialState = 'zero'; opt.Display = 'on';

## References

[1] Larimore, W.E. “Canonical variate
analysis in identification, filtering and adaptive control.”
*Proceedings of the 29th IEEE Conference on Decision and
Control*, pp. 596–604, 1990.

[2] Verhaegen, M. “Identification of the
deterministic part of MIMO state space models.”
*Automatica*, Vol. 30, 1994, pp. 61–74.

[3] Ljung, L. *System Identification:
Theory for the User*. Upper Saddle River, NJ: Prentice-Hall PTR,
1999.

[4] Jansson, M. “Subspace identification and ARX
modeling.” *13th IFAC Symposium on System Identification*,
Rotterdam, The Netherlands, 2003.

## Version History

**Introduced in R2012a**

### 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
`n4sidOptions`

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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