ssestOptions
Option set for ssest
Description
Use an ssestOptions
object to specify options for estimating
statespace models using the ssest
function. You can specify options such as
the handling of initial states, stability enforcement, and the numerical search method to be
used in estimation.
Creation
Description
Properties
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 multipleexperiment 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 values in the following
table.
Value  Description 

[]  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, specify
Passbands are expressed in
rad/ 
SISO filter  Specify a singleinputsingleoutput (SISO) linear filter in one of the following ways:

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, 
'inv'  Applicable for estimation using frequencyresponse data only. Use $$1/G(\omega )$$ as the weighting filter, where G(ω) is the complex frequencyresponse data. Use this option for capturing relatively low amplitude dynamics in data, or for fitting data with high modal density. This option also makes it easier to specify channeldependent weighting filters for MIMO frequencyresponse data. 
'invsqrt'  Applicable for estimation using frequencyresponse data only. Use $$1/\sqrt{G(\omega )}$$ as the weighting filter. Use this option for capturing relatively low amplitude dynamics in data, or for fitting data with high modal density. This option also makes it easier to specify channeldependent weighting filters for MIMO frequencyresponse data. 
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
.
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 progressviewer window.'off'
— No progress or results information is displayed.
InputInterSample
— Inputchannel intersample behavior
'auto'
 'zoh'
 'foh'
 'bl'
Inputchannel 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'
— Zeroorder hold maintains a piecewiseconstant input signal between samples.'foh'
— Firstorder hold maintains a piecewiselinear input signal between samples.'bl'
— Bandlimited behavior specifies that the continuoustime 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 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 This algorithm requires Optimization Toolbox™ software. 
'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 
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 fields in the following table.
Field Name  Description  Default  

ErrorThreshold  Error threshold at which to adjust the weight of large errors from quadratic to linear. Errors larger than
An  0  
MaxSize  Maximum number of elements in a segment when inputoutput data is split into segments.
 250000  
StabilityThreshold  Threshold for stability tests.
 
AutoInitThreshold  Threshold at which to automatically estimate initial conditions. The software estimates the initial conditions when: $$\frac{\Vert {y}_{p,z}{y}_{meas}\Vert}{\Vert {y}_{p,e}{y}_{meas}\Vert}>\text{AutoInitThreshold}$$  1.05  
DDC  Specifies if the Data Driven Coordinates algorithm [5] is used to estimate freely parameterized statespace models. Specify

Examples
Create Default Option Set for State Space Estimation
opt = ssestOptions
Option set for the ssest command: InitializeMethod: 'auto' InitialState: 'auto' N4Weight: 'auto' N4Horizon: 'auto' Display: 'off' InputInterSample: 'auto' InputOffset: [] OutputOffset: [] EstimateCovariance: 1 OutputWeight: [] Focus: 'prediction' WeightingFilter: [] EnforceStability: 0 SearchMethod: 'auto' SearchOptions: '<Optimization options set>' Regularization: [1x1 struct] Advanced: [1x1 struct]
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")
Option set for the ssest command: InitializeMethod: 'auto' InitialState: 'backcast' N4Weight: 'auto' N4Horizon: 'auto' Display: 'on' InputInterSample: 'auto' InputOffset: [] OutputOffset: [] EstimateCovariance: 1 OutputWeight: [] Focus: 'prediction' WeightingFilter: [] EnforceStability: 0 SearchMethod: 'auto' SearchOptions: '<Optimization options set>' Regularization: [1x1 struct] Advanced: [1x1 struct]
Alternatively, use dot notation to set the values of opt
.
opt = ssestOptions; opt.InitialState = "backcast"; opt.Display = "on";
References
[1] Larimore, Wallace 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, Michel. "Identification of the deterministic part of MIMO state space models given in innovations form from inputoutput data." Automatica, Vol. 30, No. 1, 1994, pp. 61–74. https://doi.org/10.1016/00051098(94)902291
[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, Lennart. System Identification: Theory for the User. Upper Saddle River, NJ: PrenticeHall PTR, 1999.
[5] McKelvey, Tomas, 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, Magnus. “Subspace identification and ARX modeling.” 13th IFAC Symposium on System Identification , Rotterdam, The Netherlands, 2003.
[7] Ozdemir, Ahmet Arda, 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 R2012aR2022b: 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
ssestOptions
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.
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