Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single‐input–single‐output fractional‐order continuous‐time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional‐order continuous‐time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non‐linearity of the Wiener model part does not need to be invertible. The input and output static non‐linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional‐order continuous‐time subsystem and the input and output static non‐linear functions from the sampled input–output data by considering the system to be a multi‐input–single‐output linear fractional‐order continuous‐time model. These extra inputs represent the basis functions of the static input and output non‐linearity, where the output basis functions are simulated according to the previous estimates of the fractional‐order linear subsystem and the static input non‐linear function at every iteration. It is also possible to estimate the classical integer‐order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer‐order continuous‐time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional‐order Hammerstein–Wiener output model.