A blind approach to identification of Hammerstein-Wiener systems corrupted by nonlinear-process noise

This paper proposes a new blind approach to identification of Hammerstein-Wiener models, where a linear dynamics is embedded between two static nonlinearities. The blind approach directly aims at estimating immeasurable inner input and output, with noise effects in consideration. By exploiting input´s piece-wise constant property, the parameters of the inverse output nonlinearity and the denominator of the linear dynamics are consistently identified via an iterative instrumental-variable based method from the output measurements only; next, a subspace direct equalization method estimates the immeasurable inner input. The blind approach does not require an explicit parametrization of the input nonlinearity; moreover, the input nonlinearities are more general than static nonlinearities and may include finite-memory nonlinearities such as hysteresisrelay and hysteresis backlash. The proposed blind approach is validated and compared with the blind approach proposed by Bai in 2002 through numerical simulations.