Time-varying autoregressive system identification using wavelets

In this paper, the problem of time-varying parametric autoregressive (AR) model identification by wavelets is discussed. 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 estimation. Utilizing multiresoulution analysis techniques, the smooth trends and the rapidly changing components of time-varying AR model parameters can both be estimated accurately. Then, the proposed MLS algorithm is combined with the Total Least Squares algorithm for noisy time-varying AR model identification. Simulation results verify the effectiveness of our algorithms.