Identification of non-parametric FIR non-linear systems with low-degree interactive terms

In this paper, an interactive term identification approach is proposed for identification of non-parametric finite impulse response non-linear systems under i.i.d. random sequences. The idea is to make a high-dimensional non-linear identification problem into a number of low-dimensional problems and thus to effectively combat the problem of the curse of dimensionality. Convergence results are established in the paper and numerical results support the theoretical analysis and demonstrate that the proposed approach is an attractive alternative to existing non-linear identification methods.