iv4
ARX model estimation using fourstage instrumental variable method
Syntax
sys = iv4(data,[na
nb nk])
sys = iv4(data,'na',na,'nb',nb,'nk',nk)
sys = iv4(___,Name,Value)
sys = iv4(___,opt)
Description
estimates an ARX polynomial model, sys
= iv4(data
,[na
nb nk]
)sys
,
using the fourstage instrumental variable method, for the data object data
. [na
nb nk]
specifies the ARX structure orders of the A and B polynomials
and the input to output delay. The estimation algorithm is insensitive
to the color of the noise term.
sys
is an ARX model:
$$A(q)y(t)=B(q)u(tnk)+v(t)$$
alternatively
specify the ARX model orders separately.sys
= iv4(data
,'na',na,'nb',nb,'nk',nk)
estimates
an ARX polynomial with additional options specified by one or more sys
= iv4(___,Name,Value
)Name,Value
pair
arguments.
uses
the option set, sys
= iv4(___,opt
)opt
, to configure the estimation
behavior.
Input Arguments

Estimation data. The data can be:


ARX polynomial orders. For multioutput model, 

Estimation options.
Use 
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.

Input delay for each input channel, specified as a scalar value
or numeric vector. For continuoustime systems, specify input delays
in the time unit stored in the For a system with You can also set Default: 0 

Transport delays. For continuoustime systems, specify transport delays in the
time unit stored in the For a MIMO system with Default: 

Specify integrators in the noise channels. Adding an integrator creates an ARIX model represented by: $$A(q)y(t)=B(q)u(tnk)+\frac{1}{1{q}^{1}}e(t)$$ where,$$\frac{1}{1{q}^{1}}$$ is the integrator in the noise channel, e(t).
Default: 
Output Arguments

ARX model that fits the estimation data, returned as a discretetime Information about the estimation results and options used is
stored in the
For more information on using 
Examples
Algorithms
Estimation is performed in 4 stages. The first stage uses the arx
function. The resulting model generates the instruments for a
secondstage IV estimate. The residuals obtained from this model are modeled as a
highorder AR model. At the fourth stage, the inputoutput data is filtered through this
AR model and then subjected to the IV function with the same instrument filters as in
the second stage.
For the multipleoutput case, optimal instruments are obtained only if the noise sources at the different outputs have the same color. The estimates obtained with the routine are reasonably accurate, however, even in other cases.
References
[1] Ljung, L. System Identification: Theory for the User, equations (15.21) through (15.26), Upper Saddle River, NJ, PrenticeHall PTR, 1999.