System Identification Toolbox™

iv4 - Estimate ARX model using four-stage instrumental variable method returning idpoly or idarx object

Syntax

m = iv4(data,orders)
m = iv4(data,'na',na,'nb',nb,'nk',nk)
m= iv4(data,orders,'Property1',Value1,...,'PropertyN',ValueN)

Description

This function is an alternative to arx and the use of the arguments is 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.

Examples

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

z = iddata(y, [u1 u2]);
nb = [2 2];
nk = [0 2];
m= 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 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.

References

Ljung (1999), equations (15.21) through (15.26).

See Also

ivx

linapp