iv4 (System Identification Toolbox)

iv4	Examples See Also

Estimate the parameters of an ARX model using an approximately optimal four-stage instrumental variable (IV) procedure.

Syntax

th = iv4(z,nn)
th = iv4(z,nn,maxsize,T)

Description

This routine is an alternative to arx and the use of the arguments are entirely analogous to the arx function. The main difference is that the procedure is not sensitive to the color of the noise term

in the model equation.

For an interpretation of the loss function (innovations covariance matrix), consult "Some Special Topics" on page 3-68 in the User's Guide.

Examples

Here is an example of a two-input one-output system with different delays on the inputs

and

z = [y u1 u2];
nb = [2 2];
nk = [0 2];
th = iv4(z,[2 nb nk]);

Algorithm

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 are filtered through this AR model and then subjected to the IV function with the same instrument-filters as in the second stage.

For the multi-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 though even in other cases.