Kernel-based identification of Wiener-Hammerstein system

This paper addresses the problem of Wiener-Hammerstein (LNL) system identification. We present two estimates, which recover the static nonlinear characteristic and the linear dynamic blocks separately. Both algorithms are based on kernel preselection of data and application of local least squares and cross-correlation techniques. Formal proofs of consistency are derived under very mild a priori restrictions imposed on the input excitation and system characteristics. In particular, the input need not be Gausssian, and a wide (nonparametric) class of nonlinear characteristics is admitted. Finally, we propose a universal multi-stage identification strategy which allows to split the resulting linear model into two separate blocks. We also present a simple simulation example to illustrate the behavior of the method in practice.