Identification of time-varying systems using multiresolution wavelet models

Abstract

Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm.

Time-varying model identification for time–frequency feature extraction from EEG data

“…Conventionally, the basis functions have been chosen to be Chebyshev and Legendre polynomials, prolate spheroidal sequences which are the best approximation to bandlimited functions [2], [4], [12]- [13] and wavelet basis that have a distinctive property of multi-resolution in both the time and frequency domains [3], [14]- [15]. Basis expansion methods have been widely applied to solve various engineering problems.…”

“…Wavelets have distinctive approximation properties and are well suited for approximating general nonstationary signals [2]- [3], [17]- [20], and thus have been successfully applied to many areas including nonlinear signal processing and parametric identification [21]- [25]. However, to our knowledge, not much work has been done to exploit the inherent approximation properties of wavelets to identify TV coefficient parameter estimation.…”

“…In this study, cardinal B-splines wavelets, which have been proved to have a lot of excellent properties, are considered and will be employed for time-varying parameter expansion. Detailed discussions about how to build the associated multi-wavelet model using B-splines can be found in [2] and [26]. .…”

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

“…An implementation, which has been tested with very good results, involves B-spline and B-wavelet functions in multiresolution wavelet decompositions (Billings and Coca 1999, Liu et al 2000, Coca and Billings 2001,Wei and Billings 2002. B-spline wavelets were originally introduced by Chui and Wang (1992) to define a class of semi-orthogonal wavelets.…”

“…Both radial wavelet networks (Zhang 1997) and multiresolution wavelet decomposition models (Billings and Coca 1999, Liu et al 2000, Coca and Billings 2001, Wei and Billings 2002 provide powerful representations for nonlinear systems. The model based on the radial wavelet frame (19), or the fixed grid wavelet network, resembles in effect the well known radial basis function (RBF) networks in structure with the Gaussian or thinspline functions replaced by radial wavelets, which can generate single scaling wavelet frames.…”