Regularized adaptive identification based on wavelet packets

In system identification, we are often encountered with a ill-posed problem of the least squares (LS) type estimation when the input signal is strongly correlated. In this paper, a new adaptive approach for identification of a finite impulse response (FIR) is investigated by utilizing the generalized wavelet decomposition (wavelet packets). In order to attain the stabilized convergence of the adaptive filters, a regularization parameter is introduced the recursive least squares (RLS) estimation of the adaptive filter weights for each wavelet packet. The analytical expression of the optimal regularization parameter and the optimal initial condition of the RLS estimation is given. The effectiveness of the proposed approach is demonstrated through simulation example.