Identification of a class of time-varying nonlinear systems using basis sequences

We consider the identification of a class of time-varying nonlinear systems, called the time-varying Hammerstein series. This identification problem is motivated by the practical need to characterise time-varying nonlinear systems in a simple and parsimonious manner. Basis sequences are introduced to facilitate a reduction in system parameterisation and also to make the estimation task tractable. A significant advantage of the approach is that only a single input-output record is required to obtain least-squares estimates of the model coefficients. The selection of basis sequences and basis order is also discussed. Simulated and real data results are presented to indicate the usefulness of the proposed identification technique. We were interested in applying the time-varying nonlinear system identification procedure to a modelling scenario in seismology.