Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter

As fractional-order models increasingly appear as an option to describe complex systems, they generate a demand for parameter estimation methods in the time and frequency domain. The extended Kalman filter (EKF) is a promising technique in the time domain, but it is sensitive to the initial conditions of the state and error covariance matrices. In the case of integer-order systems, evolutionary algorithms (EAs) can tackle EKF’s sensitiveness issues. The algorithm usually uses EAs to optimise the initial conditions for the EK, leading to a better estimate of the system parameters and states. Here, we extend this methodology to fractional-order models to estimate the model’s fractional order and parameters. Finally, we demonstrate the effectiveness of this methodology on a simple mechanical model.