AR model estimation using instrumental variable method
sys = ivar(data,na)
sys = ivar(data,na,nc)
sys = ivar(data,na,nc,max_size)
An AR model is represented by the equation:
In the above model, e(t) is an arbitrary process, assumed to be a moving average process of order nc, possibly time varying. nc is assumed to be equal to na. Instruments are chosen as appropriately filtered outputs, delayed nc steps.
Estimation time series data.
data must be an iddata object with scalar output data only.
Order of the A polynomial
Order of the moving average process representing e(t).
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.
Identified polynomial model.
sys is an AR idpoly model which encapsulates the identified polynomial model.
Compare spectra for sinusoids in noise, estimated by the IV method and by the forward-backward least squares method.
y = iddata(sin([1:500]'*1.2) + sin([1:500]'*1.5) + ... 0.2*randn(500,1),); miv = ivar(y,4); mls = ar(y,4); spectrum(miv,mls)
 Stoica, P., et al. Optimal Instrumental Variable Estimates of the AR-parameters of an ARMA Process, IEEE Trans. Autom. Control, Volume AC-30, 1985, pp. 1066–1074.