×

Asymptotic variance expressions for estimated frequency functions. (English) Zbl 1008.93064

The authors consider a parametrized set of transfer function models of a special form, \(y(t)=B(q,\theta)(F(q)^{-1}u(t)+C(q)e(t))\), where \(F\) and \(C\) are fixed polynomials, \(B\) is a polynomial with uncertain parameters and \(u\) presents an autoregression process. They derive exact expressions, nonasymptotic in the order of the model, for the variance of an estimated frequency function. This expression applies to a restricted class of models: AR-models, as well as fixed pole models with a polynomial noise model. However, a simple expression for this variance can be obtained asymptotically as the model order tends to infinity. This expression shows that the variance is inversely proportional to the signal-to-noise ratio frequency by frequency.
A numerical example and comparisons with existing results are presented.

MSC:

93E10 Estimation and detection in stochastic control theory
93C80 Frequency-response methods in control theory
93E12 Identification in stochastic control theory
PDFBibTeX XMLCite
Full Text: DOI