A Step-by-Step High-Order Extended Kalman Filter for Fractional-order System

Fractional-order systems (FOS) are characterized by strong nonlinearity, which puts forward higher criteria for state estimation. This work suggests a step-by-step high order extended Kalman filter (SHEKF) for the FOS to address this issue. Based on fractional calculus, the state model and measurement model of FOS are established, in which the nonlinear parts of both models are defined as implicit variables. Following the discovered implicit variables by Kalman filter, the linear form of the state model and measurement model are constructed. Finally, the state variables of FOS are estimated based on linearized models and prior information. The efficacy and high state estimate accuracy of the proposed method for determining the state of FOS are shown by simulation results.