Specify optional comma-separated 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.

Defines how the errors e between the measured
and the modeled outputs are weighed at specific frequencies during
the minimization of the prediction error.

Higher weighting at specific frequencies emphasizes the requirement
for a good fit at these frequencies.

Focus requires one of the following values:

'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.

'prediction' — Automatically
calculates the weighting function as a product of the input spectrum
and the inverse of the noise model. The weighting function minimizes
one-step-ahead prediction, which typically favors fitting small time
intervals (higher frequency range). From a statistical-variance point
of view, this weighting function is optimal. However, this method
neglects the approximation aspects (bias) of the fit. Use 'stability'when
you want to ensure 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
upper and lower 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.

SISO filter — Enter any SISO linear filter
in any of the following ways:

A single-input-single-output (SISO) linear system.

The {A,B,C,D} format, which specifies
the state-space matrices of the filter.

The {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 frequency-domain data
only, enter a column vector of weights for 'Focus'.
This vector must have the same size as length of 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.

Weight of prediction errors in multi-output estimation.

Specify OutputWeight as a positive semidefinite,
symmetric matrix (W). The software minimizes the
trace of the weighted prediction error matrix trace(E'*E*W). 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 multiple-input, multiple-output
models, or the reliability of corresponding data.

This option is relevant only for multi-output models.

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 positive scalar or a positive definite matrix. The
length of the matrix must be equal to the number of free parameters
(np) of the model. For ARX model, np =
sum(sum([nanb]).

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

Use arxRegul to automatically
determine Lambda and R values.

Advanced is a structure with the following
fields:

MaxSize — Specifies the
maximum number of elements in a segment when input-output 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 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
of s.

Default:0

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 z from
the origin.

Default:1+sqrt(eps)

Output Arguments

opt

Option set containing the specified options for arx.