Identification of Time-Varying Systems Using Multi-Wavelet Basis Functions

This brief introduces a new parametric modelling and identification method for linear time-varying systems using a block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be applied to track rapidly or even sharply varying processes and is developed by combining wavelet approximation theory with a block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstationary processes. Application of the proposed approach to a real mechanical system indicates better tracking capability of the multi-wavelet basis function algorithm compared with the normalized least squares or recursive least squares routines.