Parsimonious characterisation and identification of time-varying nonlinear systems

We consider the problem of time-varying nonlinear system identification when only a single observation of the input and output signals is available. In order to provide a tractable solution, the temporal and dynamic variation of the time-varying Hammerstein series is parameterised using basis sequences. This leads to a time-invariant formulation which is subsequently solved using the method of least-squares. The approach represents a practical way to characterise time-varying nonlinear phenomena in a parsimonious manner and is demonstrated with real data.