ivar (System Identification Toolbox)

ivar	Examples See Also

Estimate the parameters of an AR model using an approximately optimal choice of instrumental variable procedure.

Syntax

th = ivar(y,na)
th = ivar(y,na,nc,maxsize,T)

Description

The parameters of an AR model structure

are estimated using the instrumental variable method. y is the signal to be modeled, entered as a column vector. na is the order of the A polynomial (the number of A parameters). The resulting estimate is returned as th, in theta format. The routine is for scalar signals only.

In the above model,

is an arbitrary process, assumed to be a moving average process of order nc, possibly time varying. (Default is nc = na.) Instruments are chosen as appropriately filtered outputs, delayed nc steps.

The optional arguments maxsize and T are explained under auxvar.

Examples

Compare spectra for sinusoids in noise, estimated by the IV method and estimated by the forward-backward least-squares method:

y = sin([1:500]'*1.2) + sin([1:500]'*1.5)...
 + 0.2*randn(500,1);
thiv = ivar(y,4);
thls = ar(y,4);
giv = th2ff(thiv);
gls = th2ff(thls);
bodeplot([giv gls])