Generalized Orthonormal Basis Research Articles

Identification with Generalized Orthonormal Basis Functions - Statistical Analysis and Error Bounds

A least squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions. The basis functions are orthogonal in H2 and generalize the pulse, Laguerre and Kautz bases. One of their important properties is that when chosen properly they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only few coefficients to be estimated. Explicit bounds are derived for the bias and variance errors that occur in the parameter estimates as well as in the resulting transfer function estimates.

Modelling Linear Dynamical Systems through Generalized Orthonormal Basis Functions

In many areas of signal, system and control theory orthogonal functions play an important role in issues of analysis and design. In this paper it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems, and that compose an orthonormal basis for the signal space l2n. To this end use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of e.g. the Laguerre functions and the pulse functions, related to the use of the delay operator, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit thcsp generalized basis functions to increase the speed of convergence in a series expansion, i.e. to obtain a good approximation by retaining only a finite number of expansion coefficients.