Option set for
opt = ssestOptions
opt = ssestOptions(Name,Value)
comma-separated pairs of
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
'InitialState'— Handling of initial states
'backcast'| vector | parametric initial condition object (
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.
the initial state handling method, based on the estimation data. The
possible initial state handling methods are
Vector of doubles — Specify a column vector of length Nx, where Nx is the number of states. For multi-experiment 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 (
— Specify initial conditions by using
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
estimated together with the
idss model parameters.
Use this option only for discrete-time state-space models.
'N4Weight'— Weighting scheme used for singular-value decomposition by the N4SID algorithm
Weighting scheme used for singular-value decomposition by the N4SID algorithm, specified as one of the following values:
'MOESP' — Uses the MOESP
algorithm by Verhaegen .
'CVA' — Uses the Canonical
Variable Algorithm by Larimore .
'SSARX' — A subspace identification
method that uses an ARX estimation based algorithm to compute the
Specifying this option allows unbiased estimates when using data that is collected in closed-loop operation. For more information about the algorithm, see .
'auto' — The estimating
function chooses between the MOESP and CVA algorithms.
'N4Horizon'— Forward- and backward-prediction horizons used by the
'auto'(default) | vector
[r sy su]|
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],
r is the maximum forward prediction horizon.
The algorithm uses up to
r step-ahead predictors.
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  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
matrix means that each row of
'N4Horizon' is tried,
and the value that gives the best (prediction) fit to data is selected.
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
'Advanced'— Additional advanced options
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
0.7. For more information on robust norm choices,
see section 15.2 of .
ErrorThreshold = 0 disables
robustification and leads to a purely quadratic loss function. When
estimating with frequency-domain data, the software sets
zero. For time-domain data that contains outliers, try setting
MaxSize — Specifies the
maximum number of elements in a segment when input-output data is
split into segments.
MaxSize must be a positive integer.
StabilityThreshold — Specifies
thresholds for stability tests.
StabilityThreshold is a structure with the
s — Specifies the location
of the right-most pole to test the stability of continuous-time models.
A model is considered stable when its right-most pole is to the left
z — Specifies the maximum
distance of all poles from the origin to test stability of discrete-time
models. A model is considered stable if all poles are within the distance
AutoInitThreshold — Specifies
when to automatically estimate the initial conditions.
The initial condition is estimated when
ymeas is the measured output.
yp,z is the predicted output of a model estimated using zero initial states.
yp,e is the predicted output of a model estimated using estimated initial states.
DDC — Specifies if the Data
Driven Coordinates algorithm  is used to estimate
freely parameterized state-space models.
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
opt = ssestOptions;
Create an option set for
ssest using the
'backcast' algorithm to initialize the state and set the
opt = ssestOptions('InitialState','backcast','Display','on');
Alternatively, use dot notation to set the values of
opt = ssestOptions; opt.InitialState = 'backcast'; opt.Display = 'on';
 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.
 Verhaegen, M. “Identification of the deterministic part of MIMO state space models.” Automatica, Vol. 30, No. 1, 1994, pp. 61–74.
 Wills, Adrian, B. Ninness, and S. Gibson. “On Gradient-Based Search for Multivariable System Estimates.” Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, July 3–8, 2005. Oxford, UK: Elsevier Ltd., 2005.
 Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.
 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.
 Jansson, M. “Subspace identification and ARX modeling.” 13th IFAC Symposium on System Identification , Rotterdam, The Netherlands, 2003.