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

Abstract

In this paper, some new techniques for time-varying parametric autoregressive (AR) system identification by wavelets are presented. Firstly, we derive a new multiresolution least squares (MLS) algorithm for Gaussian time-varying AR model identification employing wavelet operator matrix representation. This method can optimally balance between the over-fitted solution and the poorly represented identification. The main features of the time-varying model parameters are estimated by a multiresoulution method, which represents 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 model. Finally, we deal with a non-Gaussian time-varying AR model for modeling nonstationary processes in a non-Gaussian distribution. A pseudo-maximum likelihood estimation algorithm is proposed for this model identification. The time-varying AR parameters as well as the non-Gaussian probability density (approximated by Gaussian mixture density) parameters of the driving noise sequence (DNS) are simultaneously estimated. Simulation results verify that our methods can effectively identify time-varying AR systems with general distributed DNS. A realistic application of the proposed technique in blind equalization of time-varying fading channel will be explored.