Recursive System Identification of Continuous-Time Fractional Systems for All Parameter Estimation

Fractional-order systems have proven to be useful to well model diffusion or propagation phenomena. Recursive or online system identification of continuous-time fractional models is explored in this article. When differentiation orders are known, only the coefficients are to be estimated: the classic recursive methods of least squares, prediction error method (PEM), and instrumental variable are adapted for fractional models. They are then compared to our new long memory PEM to prove its efficiency. When differentiation orders are unknown, which is often the case in practice, two-stage algorithms are proposed for both coefficient and differentiation order estimation. A single method of differentiation order estimation is proposed, which is then combined with the two best coefficient estimation methods (long-memory PEM and instrumental variable) to create two hybrid algorithms. The performances of these algorithms are compared through Monte Carlo simulations in order to highlight the influence of the parameter estimation in a more complex scenario. Finally, recursive identification is applied to a simulation example of a thermal lung impedance.