On identification of multivariate Hammerstein systems

This paper presents a semi-parametric approach to the problem of identification of multivariate Hammerstein systems. A nonlinearity in general multivariate Hammerstein systems is represented by projecting the d-dimensional input signal onto one dimensional subset which, in turn, is mapped by a univariate nonparametric function to an internal signal of the system. Such a parsimonious representation allows us to overcome the curse of dimensionality present in the multivariate Hammerstein system. We identify the Hammerstein system via the semi-parametric version of the least-squares. A discussion on the statistical accuracy of the resulting estimates is given. This is also verified in numerous simulation studies.