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No abstract

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This study proposes a direct parameter estimation approach from observed input-output data of a stochastic singleinput-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 continuoustime 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 nonlinear 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.