Recursive Set-Membership Parameter Estimation Using Fractional Model

Abstract

This paper deals with time-domain set-membership parameter estimation using fractional model in case of unknown-but-bounded equation error with a priori known noise bounds. In such bounded-error context, the main goal is to characterize the set of all feasible parameters compatible with the model, the measured data and some prior error bounds. The characterization is done using the outer bounding ellipsoid strategy adapted for fractional system parameters estimation. To ensure good convergence of the used algorithms, several procedures for the selection of the more suitable excitation signal and for the equation-error bound computation are proposed and discussed. When the system is commensurate, an iterative algorithm is proposed to deal with commensurate order estimation. The performances of the proposed schemes are illustrated by a numerical example via Monte Carlo simulations and through a real application of the proposed set-membership identification method on an electronic system.