tfestOptions
Option set for tfest
Description
Use a tfestOptions
object to specify options for estimating
transfer function models using the tfest
function. You can specify options such as
the estimation objective, the handling of initial conditions, and the numerical search method
to be used in estimation.
Creation
Description
creates the default
option set for estimating a transfer function model using opt
= tfestOptionstfest
. To modify the properties of this option set for your specific
application, use dot notation.
creates an option set with properties specified using one or more namevalue
arguments.opt
= tfestOptions(Name,Value
)
Properties
InitializeMethod
— Algorithm used to initialize numerator and denominator
'iv'
(default)  'svf'
 'gpmf'
 'n4sid'
 'all'
Algorithm used to initialize the values of the numerator and denominator of the
output of tfest
, specified as one of the following values:
'iv'
— Instrument Variable approach.'svf'
— State Variable Filters approach.'gpmf'
— Generalized Poisson Moment Functions approach.'n4sid'
— Subspace statespace estimation approach.'all'
— Combination of all of the preceding approaches. The software tries all these methods and selects the method that yields the smallest value of the prediction error norm.
This property is applicable only for estimation of continuoustime transfer functions using timedomain data
InitializeOptions
— Option set for initialization algorithm
structure
Option set for the initialization algorithm used to initialize the values of the
numerator and denominator of the output of tfest
, specified as a
structure with the fields in the following table.
Field Name  Description  Default  

N4Weight  Calculates the weighting matrices used in the singularvalue
decomposition step of the
 'auto'  
N4Horizon  Determines the forward and backward prediction horizons used by the
See pages 209 and 210 in [1] 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 If  'auto'  
FilterTimeConstant  Time constant of the differentiating filter used by the
$${F}_{cutoff}=\frac{\text{FilterTimeConstant}}{{T}_{s}}$$ T_{s} is the sample time of the estimation data. Specify
 0.1  
MaxIterations  Maximum number of iterations. Applicable when
InitializeMethod is 'iv' .  30  
Tolerance  Convergence tolerance. Applicable when
InitializeMethod is 'iv' .  0.01 
InitialCondition
— Handling of initial conditions
'auto'
(default)  'zero'
 'estimate'
 'backcast'
Handling of initial conditions during estimation, specified as one of the following values:
'zero'
— All initial conditions are taken as zero.'estimate'
— The necessary initial conditions are treated as estimation parameters.'backcast'
— The necessary initial conditions are estimated by a backcasting (backward filtering) process, described in [2].'auto'
— An automatic choice among the preceding options is made, guided by the data.
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
— Option to enforce stability of model
false
(default) 
true
Option to enforce stability of the estimated model, specified as
true
or false
.
Use this option when estimating models using frequencydomain data. Models estimated using timedomain data are always stable.
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 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 
Examples
Create Default Options Set for Transfer Function Estimation
opt = tfestOptions;
Specify Options for Transfer Function Estimation
Create an options set for tfest
using the 'n4sid'
initialization algorithm and set the Display
to 'on'
.
opt = tfestOptions('InitializeMethod','n4sid','Display','on');
Alternatively, use dot notation to set the values of opt
.
opt = tfestOptions; opt.InitializeMethod = 'n4sid'; opt.Display = 'on';
References
[1] Ljung, Lennart. System Identification: Theory for the User. 2nd Ed. Upper Saddle River, NJ: PrenticeHall PTR, 1999.
[2] Knudsen, T. "A New method for estimating ARMAX models," IFAC Proceedings Volumes 27, no. 8 (July 1994): 895–901. https://doi.org/10.1016/S14746670(17)478232.
[3] Wills, Adrian, B. Ninness, and S. Gibson. “On GradientBased Search for Multivariable System Estimates.” IFAC Proceedings Volumes 38, No 1 (2005): 832–837. https://doi.org/10.3182/200507036CZ1902.00140.
[4] Garnier, H., M. Mensler, and A. Richard. “Continuoustime Model Identification From Sampled Data: Implementation Issues and Performance Evaluation” International Journal of Control 76, no 13 (January 2003): 1337–57. https://doi.org/10.1080/0020717031000149636.
[5] Ljung, Lennart. “Experiments With Identification of ContinuousTime Models.” IFAC Proceedings Volumes 42, no. 10 (2009):1175–80. https://doi.org/10.3182/200907063FR2004.00195.
[6] Jansson, Magnus. “Subspace identification and ARX modeling.” IFAC Proceedings Volumes 36 no. 16 (September 2003): 1585–90. https://doi.org/10.1016/S14746670(17)349868
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