Identification of Wiener–Hammerstein systems by a nonparametric separation of the best linear approximation

Wiener–Hammerstein models are flexible, well known and often studied. The main challenge in identifying a Wiener–Hammerstein model is to distinguish the linear time invariant (LTI) blocks at the front and the back. This paper presents a nonparametric approach to separate the front and back dynamics starting from the best linear approximation (BLA). Next, the nonparametric estimates of the LTI blocks in the model can be parametrized, taking into account a phase shift degeneration. Once the dynamics are known, the estimation of the static nonlinearity boils down to a simple linear least squares problem. The consistency of the proposed approach is discussed and the method is validated on the Wiener–Hammerstein benchmark that was presented at the IFAC SYSID conference in 2009.