Time-varying system identification using an ultra-orthogonal forward regression and multiwavelet basis functions with applications to EEG

A new parametric approach is proposed for nonlinear and non-stationary system identification based on a time-varying nonlinear autoregressive with exogenous input (TV-NARX) model. The time-varying coefficients of the TV-NARX model are expanded using multi- wavelet basis functions and the model is thus transformed into a time-invariant regression problem. An ultra-orthogonal forward regression (UOFR) algorithm aided by mutual information (MI) is designed to identify a parsimonious model structure and estimate the associated model parameters. The UOFR-MI algorithm which uses not only the observed data themselves but also weak derivatives of the signals is more powerful in model structure detection. The proposed approach combining the advantages of both the basis function expansion method and the UOFR-MI algorithm is proved to be capable of tracking the change of time-varying parameters effectively in both numerical simulations and the real EEG data.