Bias-free Parameter Identification for Non-Commensurable Fractional Systems

Abstract

This paper deals with the parameter identification for non-commensurable fractional systems under noisy observations of the output signal. Fractional systems are increasingly used to describe complex systems or memory effects. Actual identification methods can not handle noisy observations of the output signal if the system is not at rest. In this paper, an approach is proposed which uses a combination of the modulating function method and the instrumental variable method. The instrumental variable method yields unbiased estimates without knowing anything about the noise which corrupts the output signal. To calculate the instrumental variables, an algorithm to calculate the closed-form solution of a fractional system is also extended by the short-memory principle. The presented approach is compared to the common least-squares method by a numerical simulation.