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Option set for tfest
opt = tfestOptions
opt = tfestOptions(Name,Value)
creates
the default option set for opt
= tfestOptionstfest
.
creates
an option set with the options specified by one or more opt
= tfestOptions(Name,Value
)Name,Value
pair
arguments.
Specify optional commaseparated 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
.
'InitMethod'
— Algorithm used to initialize the 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
, applicable
only for estimation of continuoustime transfer functions using timedomain
data, 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 prediction
error norm.
'InitOption'
— Option set for the initialization algorithmOption 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 following fields:
N4Weight
— Calculates the
weighting matrices used in the singularvalue decomposition step of
the 'n4sid'
algorithm. Applicable when InitMethod
is 'n4sid'
.
N4Weight
is specified as one of the following
values:
'MOESP'
— Uses the MOESP
algorithm by Verhaegen.
'CVA'
— Uses the canonical
variable algorithm (CVA) by Larimore.
'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 software automatically
determines if the MOESP algorithm or the CVA algorithm should be used
in the singularvalue decomposition step.
Default: ‘auto'
N4Horizon
— Determines the
forward and backward prediction horizons used by the 'n4sid'
algorithm.
Applicable when InitMethod
is 'n4sid'
.
N4Horizon
is a row vector with three elements: [r sy su]
,
where r
is the maximum forward prediction horizon.
The algorithm uses up to r
stepahead 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 [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 'N4Horizon'
a k
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 N4Horizon = 'auto'
, the software uses
an Akaike Information Criterion (AIC) for the selection of sy
and su
.
Default: 'auto'
FilterTimeConstant
— Time
constant of the differentiating filter used by the iv
, svf
,
and gpmf
initialization methods (see [4] and [5]).
FilterTimeConstant
specifies the cutoff frequency
of the differentiating filter, F_{cutoff},
as:
$${F}_{cutoff}=\frac{\text{FilterTimeConstant}}{{T}_{s}}$$
T_{s} is the sample time of the estimation data.
Specify FilterTimeConstant
as a positive
number, typically less than 1. A good value of FilterTimeConstant
is
the ratio of T_{s} to the dominating
time constant of the system.
Default: 0.1
MaxIter
— Maximum number
of iterations. Applicable when InitMethod
is 'iv'
.
Default: 30
Tolerance
— Convergence
tolerance. Applicable when InitMethod
is 'iv'
.
Default: 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 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
timedomain data and in FrequencyUnit
for frequencydomain
data, where TimeUnit
and FrequencyUnit
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 the 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.
'inv'
— Applicable for estimation
using frequencyresponse
data only. Use $$1/(G(jw))$$ as
the weighting filter. Where G(jw)
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 $$1/\sqrt{G(jw)}$$ 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 modelfalse
(default)  true
Control whether to enforce stability of estimated model, specified
as the commaseparated pair consisting of 'EnforceStability'
and
either true
or false
.
Use this option when estimating models using frequencydomain data. Models estimated using timedomain data are always stable.
Data Types: logical
'EstCovar'
— Control whether to generate parameter covariance datatrue
(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 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  matrixRemoval of offset from timedomain input data during estimation,
specified as the commaseparated 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.
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  matrixRemoval of offset from timedomain output data during estimation,
specified as the commaseparated 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.
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 matrixWeighting 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 and N
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:

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, 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 the 'noise'
or using the identity matrix
for W
.
This option is relevant for only multioutput models.
'Regularization'
— Options for regularized estimation of model parametersOptions for regularized estimation of model parameters. For more information on regularization, see Regularized Estimates of Model Parameters.
Regularization
is a structure with the following
fields:
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 zero implies no regularization.
Default: 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 np
positive numbers such that each entry denotes
the confidence in the value of the associated parameter.
The default value of 1 implies a value of eye(npfree)
,
where npfree
is the number of free parameters.
Default: 1
Nominal
— The nominal value
towards which the free parameters are pulled during estimation.
The default value of zero implies that the parameter values
are pulled towards zero. If you are refining a model, you can set
the value to 'model'
to pull the parameters towards
the parameter values of the initial model. The initial parameter values
must be finite for this setting to work.
Default: 0
'SearchMethod'
— Numerical search method used for iterative parameter estimation'auto'
(default)  'gn'
 'gna'
 'lm'
 'grad'
 'lsqnonlin'
Numerical search method used for iterative parameter estimation, specified as one of the following values:
'gn'
— The subspace GaussNewton
direction. Singular values of the Jacobian matrix less than GnPinvConst*eps*max(size(J))*norm(J)
are
discarded when computing the search direction. J is
the Jacobian matrix. The Hessian matrix is approximated by J^{T}J.
If there is no improvement in this direction, the function tries the
gradient direction.
'gna'
— An adaptive version
of subspace GaussNewton approach, suggested by Wills and Ninness [3]. Eigenvalues
less than gamma*max(sv)
of the Hessian are ignored,
where sv are the singular values of the Hessian.
The GaussNewton direction is computed in the remaining subspace. gamma has
the initial value InitGnaTol
(see Advanced
for
more information). gamma is increased by the factor LMStep
each
time the search fails to find a lower value of the criterion in less
than 5 bisections. gamma is decreased by the factor 2*LMStep
each
time a search is successful without any bisections.
'lm'
— Uses the LevenbergMarquardt
method, so that the next parameter value is pinv(H+d*I)*grad
from
the previous one, where H is the Hessian, I is
the identity matrix, and grad is the gradient. d is
a number that is increased until a lower value of the criterion is
found.
'lsqnonlin'
— Uses lsqnonlin
optimizer from Optimization Toolbox™ software.
This search method can only handle the Trace criterion.
'grad'
— The steepest descent
gradient search method.
'auto'
— A choice among
the preceding options is made in the algorithm. The descent direction
is calculated using 'gn'
, 'gna'
, 'lm'
,
and 'grad'
successively, at each iteration until
a sufficient reduction in error is achieved.
'SearchOption'
— Option set for the search algorithmOption set for the search algorithm with fields that depend
on the value of SearchMethod
.
SearchOption structure when SearchMethod is specified as 'gn', 'gna', 'lm', 'grad', or 'auto'
Field Name  Description  

Tolerance  Minimum percentage difference (divided by 100) between
the current value of the loss function and its expected improvement
after the next iteration. When the percentage of expected improvement
is less than Default:  
MaxIter  Maximum number of iterations during lossfunction minimization.
The iterations stop when Setting Use Default:  
Advanced  Advanced search settings. Specified as a structure with the following fields:

SearchOption structure when SearchMethod is specified as ‘lsqnonlin'
Field Name  Description 

TolFun  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values. The
value of Default: 
TolX  Termination tolerance on the estimated parameter values. The
value of Default: 
MaxIter  Maximum number of iterations during lossfunction minimization.
The iterations stop when The
value of Default: 
Advanced  Options set for For more information, see the Optimization Options table in Optimization Options. Use 
'Advanced'
— Additional advanced optionsAdditional 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
by 0.7
. For more information on robust norm choices,
see section 15.2 of [1].
ErrorThreshold = 0
disables
robustification and leads to a purely quadratic loss function. When
estimating with frequencydomain data, the software sets ErrorThreshold
to
zero. For timedomain data that contains outliers, try setting ErrorThreshold
to 1.6
.
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 value.
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
of s
.
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 distance z
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 InitialCondition
is 'auto'
.
Default: 1.05
opt
— Option set for tfest
tfestOptions
option setOption set for tfest
,
returned as an tfestOptions
option set.
opt = tfestOptions;
Create an options set for tfest
using the 'n4sid'
initialization algorithm and set the Display
to 'on'
.
opt = tfestOptions('InitMethod','n4sid','Display','on');
Alternatively, use dot notation to set the values of opt
.
opt = tfestOptions; opt.InitMethod = 'n4sid'; opt.Display = 'on';
[1] Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: PrenticeHall PTR, 1999.
[2] Knudsen, T. "New method for estimating ARMAX models," In Proceedings of 10th IFAC Symposium on System Identification, SYSID'94, Copenhagen, Denmark, July 1994, Vol. 2, pp. 611–617.
[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] Garnier, H., M. Mensler, and A. Richard. "Continuoustime Model Identification From Sampled Data: Implementation Issues and Performance Evaluation" International Journal of Control, 2003, Vol. 76, Issue 13, pp 1337–1357.
[5] Ljung, L. "Experiments With Identification of ContinuousTime Models." Proceedings of the 15th IFAC Symposium on System Identification. 2009.
[6] Jansson, M. "Subspace identification and ARX modeling." 13th IFAC Symposium on System Identification , Rotterdam, The Netherlands, 2003.
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