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Nonlinear system identification and prediction using orthogonal functions

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2 Author(s)
Scott, I. ; Dept. of Electr. Eng., Edinburgh Univ., UK ; Mulgrew, B.

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

Published in:

Signal Processing, IEEE Transactions on  (Volume:45 ,  Issue: 7 )