Option set for ssest
opt = ssestOptions
opt = ssestOptions(Name,Value)
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.
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
.
'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 using idpar
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 of x0obj
are
estimated together with the idss
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 strings:
'MOESP'
— Uses the MOESP
algorithm by Verhaegen [2].
'CVA'
— Uses the Canonical
Variable 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 matrixForward 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]
,
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 [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'
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 you specify N4Horizon
as a single column, r = sy = su
is used.
'auto'
— The software uses
an Akaike Information Criterion (AIC) for the selection of sy
and su
.
'Focus'
— Estimation focus'prediction'
(default)  'simulation'
 'stability'
 vector  matrix  linear systemEstimation 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 values:
'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 onestepahead prediction. This approach typically favors fitting
small time intervals (higher frequency range). From a statisticalvariance
point of view, this weighting function is optimal. However, this method
neglects the approximation aspects (bias) of the fit.
This option focuses on producing a good predictor and does not
enforce model stability. Use 'stability'
when you
want to ensure a stable model.
'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. This
method provides a stable model.
'stability'
— Same as 'prediction'
,
but with model stability enforced.
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 union of 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 SISO linear filter in one of the following ways:
A singleinputsingleoutput (SISO) linear system
{A,B,C,D}
format, which specifies
the statespace matrices of the filter
{numerator, denominator}
format,
which specifies the numerator and denominator of the filter transfer
function
This option 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 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.
'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 strings:
'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 multipleinput, multipleoutput models, or the reliability of corresponding data.
N
is the number of data samples.
This option is relevant for only multiinput, multioutput models.
[]
— The software chooses
between the 'noise'
or using the identity matrix
for W
.
'Regularization'
— Options for regularized estimation of model parametersstructureOptions 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 strings:
'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. 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 the Optimization Toolbox™ software.
This search method can only handle the Trace criterion.
'grad'
— The steepest descent
gradient search method.
'auto'
— The algorithm chooses
one of the preceding options. The descent direction is calculated
using 'gn'
, 'gna'
, 'lm'
,
and 'grad'
successively, at each iteration. The
iterations continue until a sufficient reduction in error is achieved.
'SearchOption'
— Option set for the search algorithmsearch option setOption 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 optionsstructureAdditional 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 criteria.
The standard deviation is estimated robustly as the median of the
absolute deviations from the median and divided by 0.7
.
For more information on robust norm choices, see section 15.2 of [4].
ErrorThreshold = 0
disables
robustification and leads to a purely quadratic criterion. 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.
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 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 chosen SearchMethod
.
Default: 'on'
opt
— Option set for ssest
ssestOptions
option setOption set for ssest
,
returned as an ssestOptions
option set.
opt = ssestOptions;
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';
[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.
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