Circuits, Systems, and Signal Processing

, Volume 37, Issue 9, pp 3756–3784 | Cite as

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

  • Abdolrahman Ramezani
  • Behrouz SafarinejadianEmail author


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.


Fractional-order unscented Kalman filter Nonlinear fractional-order systems State estimation Adaptive noise covariance matrix 


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Control Engineering DepartmentShiraz University of TechnologyShirazIran

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