Model-free fractional order differentiator based on modulating functions method

This paper aims to design a model-free fractional order differentiator based on the modulating functions method, which can non-asymptotically and robustly estimate fractional derivatives from discrete and noisy observation. In this paper, we adopt the idea of model approximation, and in this way, the problem of designing a differentiator is transformed into the parameter estimation problem for the approximation model. For this, a local approximation model with a short integration time is proposed. To enhance the integration effect, a moving window is introduced to increase the integration time. However, these two methods are indirect. To obtain the fractional derivative more conveniently, a direct model-free fractional differentiator is proposed. Finally, numerical simulation results are given to illustrate the efficiency and robustness of the proposed method.