System identification with generalized orthonormal basis functions

Paul M.J. Van Den Hof, Peter S.C. Heuberger, József Bokor

Research output: Contribution to journalArticle

214 Citations (Scopus)


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 a few coefficients to be estimated. Explicit bounds are derived for the bias and variance errors that occur in parameter estimates as well as in the resulting transfer function estimates.

Original languageEnglish
Pages (from-to)1821-1834
Number of pages14
Issue number12
Publication statusPublished - Dec 1995


  • FIR models
  • System identification
  • linear regression
  • modelling errors
  • orthogonal basis functions
  • system approximation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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