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System identification with generalized orthonormal basis functions. (English) Zbl 0848.93013
Linear system identification is considered by using a set of flexible basis functions for the space of stable systems that generalize the classical Laguerre and Kautz bases. A least-squares identification of a finite number of expansion coefficients in the orthogonal series expansion of a transfer function is studied, and explicit bounds for the asymptotic bias and variance errors of the parameter estimates and the resulting transfer function estimates are derived and analyzed. The important advantage of the method is that a proper choice of basis functions (reflecting the dominant dynamics of the process to be modeled) can substantially diminish the number of expansion coefficients that should be estimated in a finite-length series expansion to obtain the approximate model up to a satisfactory accuracy. An illustrative simulation example is included.
MSC:
93B30System identification
42C10Fourier series in special orthogonal functions