System Modeling Using Basis Functions and Application to Echo Cancelation

This thesis concerns modeling of linear and nonlinear dynamic systems, where the applied models can be described by basis function expansions. In the first part of the thesis, the investigated model (or filter) structures and parameter estimation algorithms are described. The focus is on the parameter estimation algorithms, for both off-line and on-line estimation. Specifically, efficient batch and recursive algorithms are proposed for estimating the parameters in neural net filters, Hammerstein models, Kautz filters and Laguerre filters. In some of the examples, recorded echoes of real telephone network channels are used, for illustrating the application of the proposed models and algorithms. The Levenberg-Marquardt algorithm has better performance than other algorithms in off-line training of neural nets. This inspires the prospect of using a recursive version of the algorithm for on-line training of neural nets for nonlinear adaptive filtering. When the estimation of Hammerstein models, Kautz filters and Laguerre filters is based on a minimization of the least-squares error criterion, the minimization problem becomes separable with respect to the linear parameters. The proposed batch and recursive algorithms are derived using such separable nonlinear least-squares method. In the second part of the thesis, the methods to solve the acoustic echo cancelation problems are presented. FIR filters are commonly used in acoustic echo cancelers, because of their simple structure. However, the filters are ineffective filter structures for approximating an echo system, due to their many required parameters. The Kautz and Laguerre filters can be the possible solutions, because they can accurately describe a slowly decaying impulse response with few parameters. The acoustic echo system is physically formed by possibly a nonlinearly distorted sound source, in series with a room impulse response. This motivates the proposal of using cascaded filters as the filter structures in nonlinear echo cancelers. The cascaded filter consists of a nonlinear model concatenated with a linear FIR filter.