Time-varying parametric system multiresolution identification by wavelets

In this paper, the problem of time-varying parametric system identification by wavelets is discussed. Employing wavelet operator matrix representation , we propose a new multiresolution least squares (MLS) algorithm for time-v arying AR (ARX) system identification and a multiresolution least mean squa res (MLMS) algorithm for the refinement of parameter estimation. These tech niques can achieve the optimal trade-off between the over-fitted solution a nd the poorly represented identification. The main features of time-varying model parameters are extracted in a multiresolution way, which can be used to represent the smooth trends as well as track the rapidly changing compo nents of time-varying parameters simultaneously and adaptively. Further, a noisy time-varying AR (ARX) model can also be identified by combining the t otal least squares algorithm with the MLS algorithm. Based on the proposed AR (ARX) model parameter estimation algorithm, a novel identification schem e for time-varying ARMA (ARMAX) system is presented. A higher-order time-va rying AR (ARX) model is used to approximate the time-varying ARMA (ARMAX) s ystem and thus obtain an initial parameter estimation. Then an iterative al gorithm is applied to obtain the consistent and efficient estimates of the ARMA (ARMAX) system parameters. This ARMA (ARMAX) identification algorithm requires linear operations only and thus greatly saves the computational lo ad. In order to determine the time-varying model order, some modified AIC a nd MDL criterions are developed based on the proposed wavelet identificatio n schemes. Simulation results verify that our methods can track the rapidly changing of time-varying system parameters and attain the best balance bet ween parsimonious modelling and accurate identification.