A fractional high-order extended Kalman filter for fractional-order nonlinear systems

A fractional high-order extended kalman filter (FHEKF) algorithm for a fractional-order nonlinear system is presented. Firstly, the nonlinear function is expanded into a high-order Taylor series with the estimation error as the variable. Then, each high-order polynomial term in the Taylor series is defined as a hidden variable, and the corresponding linear dynamic model is established. Consequently, the state estimation of the original system is reconstructed by combining the estimation of the prediction error and the state prediction. Simulation experiments were carried out to select the optimal order of the Taylor expansion, enumerating the first to fourth-order expressions of the Taylor expansion, and the results show that the third-order Taylor expansion has the highest timeliness. In the motor dynamic process state estimation experiment, the dynamic following and anti-interference performance of the FHEKF (3rd order) with three other filters are compared, and the results prove the effectiveness of the method in this paper.