Nonlinear System Identification and Prediction using Orthonormal Functions

I. Scott, Bernie Mulgrew

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We describe a systematic scheme for the nonlinear adaptive filtering of signals that are generated by nonlinear dynamical systems. The complete filter consists of three sections: a signal-independent standard orthonormal expansion, a scaling derived from an estimate of the vector probability density function (PDF), and an adaptive linear combiner. The orthonormal property of the expansions has two significant implications for adaptive filtering: first, model order reduction is trivial since the contribution of each term to the mean squared error is directly related to the coefficient in the final linear combiner; and second, consistent and rapid convergence of stochastic gradient algorithms is assured. A technique based on the inverse Fourier transform for obtaining a PDF estimate from the characteristic function is also presented. The prediction and identification performance of this nonlinear structure is examined for a number of signals, and it is contrasted with common radial basis function and linear networks
Original languageEnglish
Pages (from-to)1842-1853
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number7
Publication statusPublished - Jul 1997

Keywords / Materials (for Non-textual outputs)

  • Adaptive filters
  • Convergence
  • Filtering algorithms
  • Nonlinear dynamical systems
  • Nonlinear filters
  • Nonlinear systems
  • Probability density function
  • Signal generators
  • Stochastic processes
  • Vectors


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