A weighting method for approximate nonlinear system identification

Many approximation results in nonlinear system identification concern particular signal distributions. This seems to limit the applicability of these results to cases where the relevant signals have these distributions. However, by using a weighting method that modifies the cost function used in the identification method, the available approximation results can be used also for rather general classes of signal distributions. The purpose of this paper is to describe this weighting approach and to point at some interesting application areas within nonlinear system identification. In particular, it will be described how the impulse response of a Hammerstein system can be estimated consistently for an arbitrary input signal.