Identification of time-varying Hammerstein systems

We consider the identification of systems which are both time-varying and nonlinear. This class of systems is more likely to be encountered in practice, but is often avoided due to the difficulties that arise in modelling and estimation. We attempt to address this problem by considering a new time-varying nonlinear model, the time-varying Hammerstein model, which effectively characterises time-variation and nonlinearity in a simple manner. Using this model we formulate a procedure to find least-squares estimates of the coefficients. The model is general and can be used when little is known about the time-variation of the system. In addition, we do not require that the input is stationary or Gaussian. Finally, an application to automobile knock modelling is presented, where a time-varying nonlinear model is seen to more accurately characterise the system than a time-varying linear one