Using a Wiener Filter to Estimate a Transfer Function As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, 


How would you put a minimum MSE criteria on how well the estimated filter weights matched the actual transfer function of the system? [Suppose you needed the MSE to be no more than -50dB]?
How would you change his formulation if you wanted poles as well as zeroes (an IIR rather than an FIR filter)?
The desired MSE is application dependent, so there can be no general
rule. If the approximation doesn't satisfy your needs you can
increase the filter length to obtain a better match.
There is no straightforward way to change the FIR Wiener filter solution to an IIR solution because the IIR formulation results in a set of nonlinear equations which have no closed-form solution. The IIR solution might also be unstable, so FIR filters are a much more practical choice when computing a Wiener filter.