Long Memory Recursive Prediction Error Method for Identification of Continuous-time Fractional Models

Abstract This paper deals with recursive continuoustime system identification using fractional differentiation models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional order models. When differentiation orders are assumed known, least-squares and prediction error methods, being direct extensions of the classic methods used for integer order models, are compared to our new method, thus proving the efficiency of our algorithms. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation order estimation. The performances of the new proposed recursive algorithm is studied through Monte-Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfer in lungs is modeled by using thermal two-port network formalism with fractional models.