System Identification

Hello All,

There is a physical system which is described well by the 2nd order pole 
  only model. The poles can be complex (Q up to 10), or real, including 
the degenerated cases with one pole or no poles at all. The impulse 
response can be measured.

The problem is to find the system parameters from the impulse response 
as accurate as possible. There are methods based on the Bode plots, 
min/max peaks, slopes, zero crossing position estimations. However they 
look pretty much ad-hoc, require the initial decision about the system 
type, and prone to errors.

I made the AR estimator: compute the autocorrelation function, then 
Levinson-Durbin to get the model coefficients, then solve for the poles. 
However it appears that the result is dependent on the sample rate, 
especially in the case of low Q poles. This is not a numeric issue. The 
result could be completely wrong with the higher oversampling, and this 
looks to be the problem of the approach.

What would be the right way to estimate the parameters?


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com