A Modified Fractional-Order Unscented Kalman Filter for Nonlinear Fractional-Order Systems

In this paper, a fractional-order unscented Kalman filter (FUKF) is introduced at first. Then, its convergence is analyzed based on Lyapunov functions for nonlinear fractional-order systems. Specific conditions are obtained that guarantee the boundedness of the FUKF estimation error. In addition, an adaptive noise covariance is suggested to overcome huge estimation errors. Since the adaptation law plays a crucial role in the performance of the proposed method, a fuzzy logic based method is also presented to improve the adaptive noise covariance. Therefore, a modified FUKF is proposed to increase the convergence and the accuracy of the estimation. Finally, the proposed algorithm is implemented to estimate the states of a two electric pendulum system and its performance is analyzed. Simulation results show that a huge estimation error leads to the FUKF divergence; however, the modified fractional-order unscented Kalman filter with fuzzy performs an accurate state estimation.