Bias-free Parameter Identification of a Fractional Order Model

Abstract

This paper deals with the parameter identification of a fractional system considering a noisy observation of the output signal. The novelty is that the instrumental variable method is applied to the modulating function method applied to a fractional system. A simulated output signal which is not correlated to noise is required as the instrumental variable. Because all known simulation algorithms only consider zero initial conditions, the simulated output signal converges against the true output signal in an undefined time if the zero initial conditions are penalized. Therefore, an algorithm is extended with the short-memory principle. The benefit is that after a fixed time the error between the simulated and true output signal is small and can be used as the instrumental variable. Considering this extension of the simulation algorithms, it is shown that a consistent estimation is yield with the instrumental variable method.