SYSTEM-IDENTIFICATION WITH GENERALIZED ORTHONORMAL BASIS FUNCTIONS

A least-squares identification method is studied that estimates a fini te number of expansion coefficients in the series expansion of a trans fer function, where the expansion is in terms of recently introduced g eneralized basis functions. The basis functions are orthogonal in H-2, and generalize the pulse, Laguerre and Kautz bases. One of their impo rtant 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 a few coefficients to be est imated. Explicit bounds are derived for the bias and variance errors t hat occur in parameter estimates as well as in the resulting transfer function estimates.