ssestOptions
Option set for ssest
Syntax
opt = ssestOptions
opt = ssestOptions(Name,Value)
Description
creates
the default option set for opt
= ssestOptionsssest
.
creates an option set with the options specified by one or more
opt
= ssestOptions(Name,Value
)Name,Value
pair arguments.
Input Arguments
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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.
InitializeMethod
— Algorithm used to initialize the statespace parameters
'auto'
(default)  'n4sid'
 'lsrf'
Algorithm used to initialize the statespace parameter values for
ssest
, specified as one of the following
values:
'auto'
—ssest
selects automatically:lsrf
, if the system is nonMIMO, the data is frequencydomain, and the statespace parameters are realvalued.n4sid
otherwise (timedomain, MIMO, or with complexvalued statespace parameters).
'n4sid'
— Subspace statespace estimation approach — can be used with all systems (seen4sid
).'lsrf'
— Leastsquares rational function estimationbased approach [7] (see ContinuousTime Transfer Function Estimation Using ContinuousTime FrequencyDomain Data) — can provide higheraccuracy results for nonMIMO frequencydomain systems with realvalued statespace parameters, but cannot be used for any other systems (timedomain, MIMO, or with complexvalued statespace parameters).
InitialState
— Handling of initial states
'auto'
(default)  'zero'
 'estimate'
 'backcast'
 vector  parametric initial condition object
(x0obj
)
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.'backcast'
— The initial state is estimated using the best least squares fit.'auto'
—ssest
chooses the initial state handling method, based on the estimation data. The possible initial state handling methods are'zero'
,'estimate'
and'backcast'
.Vector of doubles — Specify a column vector of length Nx, where Nx is the number of states. For multiexperiment data, specify a matrix with Ne columns, where Ne is the number of experiments. The specified values are treated as fixed values during the estimation process.
Parametric initial condition object (
x0obj
) — Specify initial conditions by usingidpar
to create a parametric initial condition object. You can specify minimum/maximum bounds and fix the values of specific states using the parametric initial condition object. The free entries ofx0obj
are estimated together with theidss
model parameters.Use this option only for discretetime statespace models.
N4Weight
— Weighting scheme used for singularvalue decomposition by the N4SID algorithm
'auto'
(default)  'MOESP'
 'CVA'
 'SSARX'
Weighting scheme used for singularvalue 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].'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 closedloop operation. For more information about the algorithm, see [6].
'auto'
— The estimating function chooses between the MOESP and CVA algorithms.
N4Horizon
— Forward and backwardprediction horizons used by the N4SID
algorithm
'auto'
(default)  vector [r sy su]
 k
by3 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]
, wherer
is the maximum forward prediction horizon. The algorithm uses up tor
stepahead predictors.sy
is the number of past outputs, andsu
is the number of past inputs that are used for the predictions. See pages 209 and 210 in [4] 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'
ak
by3 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 ofsy
andsu
.
Focus
— Error to be minimized
'prediction'
(default)  'simulation'
Error to be minimized in the loss function during estimation,
specified as the commaseparated pair consisting of 'Focus'
and
one of the following values:
'prediction'
— The onestep 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  'inv'
'invsqrt'
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]
wherewl
andwh
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 timedomain data and inFrequencyUnit
for frequencydomain data, whereTimeUnit
andFrequencyUnit
are the time and frequency units of the estimation data.SISO filter — Specify a singleinputsingleoutput (SISO) linear filter in one of the following ways:
A SISO LTI model
{A,B,C,D}
format, which specifies the statespace 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 frequencydomain 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.'invsqrt'
— Applicable for frequencydomain data only, withInitializeMethod
set to'lsrf'
only. Uses $$1/\sqrt{G(\omega )}$$ as the weighting filter, where G(ω) is the complex frequencyresponse data. Use this option for capturing relatively low amplitude dynamics in data.'inv'
— Applicable for frequencydomain data only, withInitializeMethod
set to'lsrf'
only. Uses $$1/G(\omega )$$ as the weighting filter. Similarly to'invsqrt'
, this option captures relatively lowamplitude dynamics in data. Use it when'invsqrt'
weighting produces an estimate that is missing dynamics in the lowamplitude regions.'inv'
is more sensitive to noise than'invsqrt'
.
EnforceStability
— Control whether to enforce stability of model
false
(default)  true
Control whether to enforce stability of estimated model, specified
as the commaseparated pair consisting of 'EnforceStability'
and
either true
or false
.
Data Types: logical
EstimateCovariance
— Control whether to generate parameter covariance data
true
(default)  false
Controls whether parameter covariance data is generated, specified as
true
or false
.
If EstimateCovariance
is true
, then use
getcov
to fetch the covariance matrix
from the estimated model.
Display
— Specify whether to display estimation progress
'off'
(default)  'on'
Specify whether to display the estimation progress, specified as one of the following values:
'on'
— Information on model structure and estimation results are displayed in a progressviewer window.'off'
— No progress or results information is displayed.
InputOffset
— Removal of offset from timedomain input data during estimation
[]
(default)  vector of positive integers  matrix
Removal of offset from timedomain 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.NubyNe matrix — For multiexperiment data, specify
InputOffset
as an NubyNe 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 timedomain output data during estimation
[]
(default)  vector  matrix
Removal of offset from timedomain 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.NybyNe matrix — For multiexperiment data, specify
OutputOffset
as a NybyNe 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 multioutput estimations
[]
(default)  'noise'
 positive semidefinite symmetric matrix
Weighting of prediction errors in multioutput estimations, specified as one of the following values:
'noise'
— Minimize $$\mathrm{det}(E\text{'}*E/N)$$, where E represents the prediction error andN
is the number of data samples. This choice is optimal in a statistical sense and leads to maximum likelihood estimates if nothing is known about the variance of the noise. It uses the inverse of the estimated noise variance as the weighting function.Note
OutputWeight
must not be'noise'
ifSearchMethod
is'lsqnonlin'
.Positive semidefinite symmetric matrix (
W
) — Minimize the trace of the weighted prediction error matrixtrace(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 multipleoutput models, or the reliability of corresponding data.
N
is the number of data samples.
[]
— The software chooses between'noise'
and using the identity matrix forW
.
This option is relevant for only multioutput models.
Regularization
— Options for regularized estimation of model parameters
structure
Options for regularized estimation of model parameters, specified as a structure with the fields in the following table. For more information on regularization, see Regularized Estimates of Model Parameters.
Field Name  Description  Default 

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 0 implies no regularization.  0 
R  Weighting matrix. Specify a vector of nonnegative numbers or a square positive semidefinite matrix. The length must be equal to the number of free parameters of the model. For blackbox models, using the default value is
recommended. For structured and greybox models, you can also
specify a vector of The default value of 1 implies a value of
 1 
Nominal  The nominal value towards which the free parameters are pulled during estimation. The default value of 0 implies that
the parameter values are pulled towards zero. If you are refining a
model, you can set the value to  0 
SearchMethod
— Numerical search method used for iterative parameter estimation
'auto'
(default)  'gn'
 'gna'
 'lm'
 'grad'
 'lsqnonlin'
 'fmincon'
Numerical search method used for iterative parameter estimation, specified as the one of the values in the following table.
SearchMethod  Description 

'auto'  Automatic method selection A combination of the
line search algorithms, 
'gn'  Subspace GaussNewton leastsquares search. Singular values of the Jacobian matrix less than

'gna'  Adaptive subspace GaussNewton search. Eigenvalues
less than 
'lm'  LevenbergMarquardt least squares search Each
parameter value is 
'grad'  Steepest descent leastsquares search. 
'lsqnonlin'  Trustregionreflective algorithm of

'fmincon'  Constrained nonlinear solvers. You can use the
sequential quadratic programming (SQP) and trustregionreflective
algorithms of the

SearchOptions
— Option set for search algorithm
search option set
Option set for the search algorithm, specified as a search option set with fields that
depend on the value of SearchMethod
.
SearchOptions
Structure When SearchMethod
is Specified
as 'gn'
, 'gna'
, 'lm'
,
'grad'
, or 'auto'
Field Name  Description  Default  

Tolerance  Minimum percentage difference between the current value
of the loss function and its expected improvement after the next iteration,
specified as a positive scalar. When the percentage of expected improvement
is less than  0.01  
MaxIterations  Maximum number of iterations during lossfunction minimization, specified as a positive
integer. The iterations stop when Setting
Use
 20  
Advanced  Advanced search settings, specified as a structure with the following fields:

SearchOptions
Structure When SearchMethod
is Specified
as 'lsqnonlin'
Field Name  Description  Default 

FunctionTolerance  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar. The
value of  1e5 
StepTolerance  Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of  1e6 
MaxIterations  Maximum number of iterations during lossfunction minimization, specified as a positive
integer. The iterations stop when The value of
 20 
Advanced  Advanced search settings, specified as an option set
for For more information, see the Optimization Options table in Optimization Options (Optimization Toolbox).  Use optimset('lsqnonlin') to create a default
option set. 
SearchOptions
Structure When SearchMethod
is Specified
as 'fmincon'
Field Name  Description  Default 

Algorithm 
For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox).  'sqp' 
FunctionTolerance  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.  1e6 
StepTolerance  Termination tolerance on the estimated parameter values, specified as a positive scalar.  1e6 
MaxIterations  Maximum number of iterations during loss function minimization, specified as a positive
integer. The iterations stop when  100 
Advanced
— Additional advanced options
structure
Additional advanced options, specified as a structure with the following fields:
ErrorThreshold
— Specifies when to adjust the weight of large errors from quadratic to linear.Errors larger than
ErrorThreshold
times the estimated standard deviation have a linear weight in the loss function. The standard deviation is estimated robustly as the median of the absolute deviations from the median of the prediction errors, divided by0.7
. For more information on robust norm choices, see section 15.2 of [4].ErrorThreshold = 0
disables robustification and leads to a purely quadratic loss function. When estimating with frequencydomain data, the software setsErrorThreshold
to zero. For timedomain data that contains outliers, try settingErrorThreshold
to1.6
.Default:
0
MaxSize
— Specifies the maximum number of elements in a segment when inputoutput 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 rightmost pole to test the stability of continuoustime models. A model is considered stable when its rightmost pole is to the left ofs
.Default:
0
z
— Specifies the maximum distance of all poles from the origin to test stability of discretetime models. A model is considered stable if all poles are within the distancez
from the origin.Default:
1+sqrt(eps)
AutoInitThreshold
— Specifies when to automatically estimate the initial conditions.The initial condition is estimated when
$$\frac{\Vert {y}_{p,z}{y}_{meas}\Vert}{\Vert {y}_{p,e}{y}_{meas}\Vert}>\text{AutoInitThreshold}$$
y_{meas} is the measured output.
y_{p,z} is the predicted output of a model estimated using zero initial states.
y_{p,e} is the predicted output of a model estimated using estimated initial states.
Applicable when
InitialState
is'auto'
.Default:
1.05
DDC
— Specifies if the Data Driven Coordinates algorithm [5] is used to estimate freely parameterized statespace models.Specify
DDC
as one of the following values:'on'
— The free parameters are projected to a reduced space of identifiable parameters using the Data Driven Coordinates algorithm.'off'
— All the entries of A, B, and C updated directly using the chosenSearchMethod
.
Default:
'on'
Output Arguments
opt
— Option set for ssest
ssestOptions
option set
Option set for ssest
,
returned as an ssestOptions
option set.
Examples
Create Default Option Set for State Space Estimation
opt = ssestOptions;
Specify Options for State Space Estimation
Create an option set for ssest
using the 'backcast'
algorithm to initialize the state and set the Display
to 'on'
.
opt = ssestOptions('InitialState','backcast','Display','on');
Alternatively, use dot notation to set the values of opt
.
opt = ssestOptions; opt.InitialState = 'backcast'; 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, No. 1, 1994, pp. 61–74.
[3] Wills, Adrian, B. Ninness, and S. Gibson. “On GradientBased Search for Multivariable System Estimates.” Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, July 3–8, 2005. Oxford, UK: Elsevier Ltd., 2005.
[4] Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: PrenticeHall PTR, 1999.
[5] McKelvey, T., A. Helmersson,, and T. Ribarits. “Data driven local coordinates for multivariable linear systems and their application to system identification.” Automatica, Volume 40, No. 9, 2004, pp. 1629–1635.
[6] Jansson, M. “Subspace identification and ARX modeling.” 13th IFAC Symposium on System Identification , Rotterdam, The Netherlands, 2003.
[7] Ozdemir, A. A., and S. Gumossoy. "Transfer Function Estimation in System identification Toolbox via Vector Fitting." Proceedings of the 20th World Congress of the International Federation of Automatic Control. Toulouse, France, July 2017.
Version History
Introduced in R2012aR2018a: 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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