ARX model estimation using four-stage instrumental variable method
sys = iv4(data,[na
sys = iv4(data,'na',na,'nb',nb,'nk',nk)
sys = iv4(___,Name,Value)
sys = iv4(___,opt)
estimates an ARX polynomial model,
sys = iv4(
using the four-stage instrumental variable method, for the data object
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:
Estimation data. The data can be:
ARX polynomial orders.
For multi-output model,
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Input delay for each input channel, specified as a scalar value
or numeric vector. For continuous-time systems, specify input delays
in the time unit stored in the
For a system with
You can also set
For continuous-time systems, specify transport delays in the
time unit stored in the
For a MIMO system with
Specify integrators in the noise channels.
Adding an integrator creates an ARIX model represented by:
where, is the integrator in the noise channel, e(t).
ARX model that fits the estimation data, returned as a discrete-time
Information about the estimation results and options used is
stored in the
For more information on using
Estimate ARX Model Using Four-Stage Instrumental Variable Method
Load estimation data.
This data has two inputs,
u2, and one output,
Specify the ARX model orders, using the same orders for both inputs.
na = 2; nb = [2 2];
Specify a delay of
2 samples for input
u2 and no delay for input
nk = [0 2];
Estimate an ARX model using the four-stage instrumental variable method.
m = iv4(z7,[na nb nk]);
Estimation is performed in 4 stages. The first stage uses the
arx function. The resulting model generates the instruments for a
second-stage IV estimate. The residuals obtained from this model are modeled as a
high-order AR model. At the fourth stage, the input-output 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 multiple-output 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.
 Ljung, L. System Identification: Theory for the User, equations (15.21) through (15.26), Upper Saddle River, NJ, Prentice-Hall PTR, 1999.