Nonlinearity Recovering in Hammerstein System from Short Measurement Sequence

The problem of data pre-filtering for nonparametric identification of Hammerstein system from short (finite) data set is considered. The two-stage method is proposed. First, the linear dynamic block is identified using instrumental variables technique, and the inverse of the obtained model is used for output filtering. Next, the standard procedure of nonparametric regression function estimation (kernel-based, or using orthogonal series expansion) is applied, involving the filtered output sequence instead of the original one. It is shown, that for small and moderate number of data, the estimation error can be significantly reduced in comparison with standard nonparametric methods. The asymptotic properties of the method (consistency and rate of convergence) remain the same as in the classical versions of nonparametric algorithms.