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# ivx

ARX model estimation using instrumental variable method with arbitrary instruments

## Syntax

sys = ivx(data,[na nb nk],x)
sys = ivx(data,[na nb nk],x,max_size)

## Description

sys = ivx(data,[na nb nk],x) estimates an ARX polynomial model, sys, using the instrumental variable method with arbitrary instruments. The model is estimated for the time series data data. [na nb nk] specifies the ARX structure orders of the A and B polynomials and the input to output delay, expressed in the number of samples.

An ARX model is represented as:

$A\left(q\right)y\left(t\right)=B\left(q\right)u\left(t-nk\right)+v\left(t\right)$

sys = ivx(data,[na nb nk],x,max_size) specifies the maximum size of matrices formed during estimation.

## Input Arguments

 data Estimation time series data. data must be an iddata object and can represent either time- or frequency-domain data. If using frequency domain data, the number of outputs must be 1. [na nb nk] ARX model orders. For more details on the ARX model structure, see arx. x Instrument variable matrix. x is a matrix containing the arbitrary instruments for use in the instrumental variable method. x must be of the same size as the output data, data.y. For multi-experiment data, specify x as a cell array with one entry for each experiment. The instruments used are analogous to the regression vector, with y replaced by x. max_size Maximum matrix size. max_size specifies the maximum size of any matrix formed by the algorithm for estimation. Specify max_size as a reasonably large positive integer. Default: 250000

## Output Arguments

 sys Identified polynomial model. sys is an ARX idpoly model which encapsulates the identified polynomial model. ivx does not return any estimated covariance information for sys.

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### Tips

• Use iv4 first for IV estimation to identify ARX polynomial models where the instruments x are chosen automatically. Use ivx for nonstandard situations. For example, when there is feedback present in the data, or, when other instruments need to be tried. You can also use iv to automatically generate instruments from certain custom defined filters.

## References

[1] Ljung, L. System Identification: Theory for the User, page 222, Upper Saddle River, NJ, Prentice-Hal PTR, 1999.