SYSTEM-IDENTIFICATION USING KAUTZ MODELS

In this paper, the problem of approximating a linear time-invariant st able system by a finite weighted sum of given exponentials is consider ed. System identification schemes using Laguerre models are extended a nd generalized to Kautz models, which correspond to representations us ing several different possible complex exponentials. In particular, li near regression methods to estimate this sort of model from measured d ata are analyzed. The advantages of the proposed approach are the simp licity of the resulting identification scheme and the capability of mo deling resonant systems using few parameters. The subsequent analysis is based on the result that the corresponding linear regression normal equations have a block Toeplitz structure. Several results on transfe r function estimation are extended to discrete Kautz models, for examp le, asymptotic frequency domain variance expressions.