ssregestOptions

Option set for `ssregest`

Syntax

• `options = ssregestOptions` example
• `options = ssregestOptions(Name,Value)` example

Description

example

````options = ssregestOptions` creates a default option set for `ssregest`.```

example

````options = ssregestOptions(Name,Value)` specifies additional options using one or more `Name,Value` pair arguments.```

Examples

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Create Default Options 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 options 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');`

Input Arguments

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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`.

Example: `opt = ssregestOptions('InitialState','zero')` fixes the value of the initial states to zero.

`'InitialState'` — Specify handling of initial states during estimation`'estimate'` (default) | `'zero'`

Specify handling of initial states during estimation, specified as one of the following strings:

• `'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`.

`'RegulKernel'` — 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 strings:

• `'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

`'Reduction'` — Options for model order reductionstructure

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` 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'` — Estimation focus`'prediction'` (default) | `'simulation'` | vector | matrix | linear system

Estimation 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:

• `'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, which typically favors fitting small time intervals (higher frequency range). From a statistical-variance point of view, this weighting function is optimal.

This option focuses on producing a good predictor.

• `'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.

• 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 the 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 function.

This format 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.

Higher weighting at specific frequencies emphasizes the requirement for a good fit at these frequencies.

`'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 | matrix

Removal 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 multiexperiment 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 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 multiexperiment 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'` — Criterion used during minimization`[]` (default) | `'noise'` | positive semidefinite symmetric matrix

Specifies criterion used during minimization, specified as one of the following:

• `'noise'` — Minimize $\mathrm{det}\left(E\text{'}*E\right)$, where E represents the prediction error. 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)`. `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-input, multiple-output models, or the reliability of corresponding data.

This option is relevant only for multi-input, multi-output models.

• `[]` — The software chooses between the `'noise'` or using the identity matrix for `W`.

`'Advanced'` — Maximum allowable size of Jacobian matrices and choice of search methodstructure

Maximum allowable size of Jacobian matrices and choice of search method, 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 strings:

• `'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. Requires Optimization Toolbox™ software.

• `'gn'`: Quasi-Newton line search

Default: `'fmincon'`

If you do not have the Optimization Toolbox software, the default is `'gn'`.

Output Arguments

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`options` — Options set for `ssregest``ssregestOptions` options set

Estimation options for `ssregest`, returned as an `ssregestOptions` options 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.