Parameter Estimation of Hybrid Fractional-Order Hammerstein-Wiener Box-Jenkins Models Using RIVCF Method

Abstract

This paper proposes a parameter estimation algorithm for A hybrid Box-Jenkins model where the fractional-order Hammerstein-Wiener continuous-time (HWFC) system represent the noise-free system corrupted by coloured noise generated by a discrete-time integer-order sub-model. The HWFC consist of input static nonlinear, continuous-time fractional-order linear and output static nonlinear sub-models. In this paper, the simplified refined instrumental variable algorithm is extended to estimate the system parameters with the existence of the discrete-time integer-order sub-model which described by auto-regressive moving average (ARMA) process. Measured input-output data is used for parameterizing the model with fewer conditions and assumptions, for example, the static nonlinearity of the Wiener part is not required to be invertible. The proposed approach estimates the parameters of the nonlinear and linear sub-models in an iterative manner. Monte Carlo simulation analysis shows the proposed algorithm provides accurate and fast converged estimates of the fractional-order Hammerstein-Wiener hybrid Box-Jenkins model.