Modeling general distributed nonstationary process and identifying time-varying autoregressive system by wavelets: theory and application

In this paper, some new techniques for time-varying parametric autoregressi ve (AR) system identification by wavelets are presented. Firstly, we derive a new multiresolution least squares (MLS) algorithm for Gaussian time-vary ing AR model identification employing wavelet operator matrix representatio n. This method can optimally balance between the over-fitted solution and t he poorly represented identification. The main features of the time-varying model parameters are estimated by a multiresoulution method, which represe nts the smooth trends as well as the rapidly changing components. Combining the total least squares algorithm with the MLS algorithm, a new method is presented which can make the identification of a noisy time-varying AR mode l. Finally, we deal with a non-Gaussian time-varying AR model for modeling nonstationary processes in a non-Gaussian distribution. A pseudo-maximum li kelihood estimation algorithm is proposed for this model identification, Th e time-varying AR parameters as well as the non-Gaussian probability densit y (approximated by Gaussian mixture density) parameters of the driving nois e sequence (DNS) are simultaneously estimated. Simulation results verify th at our methods can effectively identify time-varying AR systems with genera l distributed DNS. A realistic application of the proposed technique in bli nd equalization of time-varying fading channel will be explored. (C) 2001 E lsevier Science B.N. All rights reserved.