Algorithm Analysis And Design Research On Unscented Kalman Filters For Continuous-time Nonlinear Fractional-order Systems

The unscented Kalman filter is an optimal observer for state estimation in the case of noise and interference.It is not only widely used for state estimation of integer-order systems,but also widely used to estimate state information of fractional-order systems.The unscented Kalman filter can effectively solve the interference problem of nonlinear functions and the state estimation problem of nonlinear fractional-order systems with noises.This paper mainly realizes the following aspects:(1)The problems of unscented Kalman filter for continuous-time nonlinear fractionalorder systems are studied for the problems of uncorrelated process and measurement noises.The Gr ¨unwald-Letnikov difference method is used to discretize equations with fractional-order nonlinear systems and obtain the difference equations of the system.In this paper,the unscented Kalman filter algorithm of the fractional-order system is proposed and solves the problem of state estimation with non-differentiable functions in such systems.(2)For the problems of uncorrelated processes and measurement noises,the hybrid extendedunscented Kalman filter design problem for continuous-time nonlinear fractional-order systems is studied.Discretization of the nonlinear fractional-order systems studied by Gr ¨unwaldLetnikov difference and fractional-order average derivative methods are used.The nonlinear functions described by the system are applied to the extended Kalman filter and the unscented Kalman filter.The first-order Taylor expansion and unscented transformation methods are used for the current moment and the previous moment,respectively.Combining the advantages of the two types of Kalman filters,the hybrid extended-unscented Kalman filter based on fractional-order average derivative algorithm can obtain more satisfactory state estimation results and improve the state estimation accuracy.Meanwhile,the hybrid extended-unscented Kalman filter can solve the uncorrelated noise problems of nonlinear fractional-order systems.(3)The problems of unscented Kalman filter for continuous-time nonlinear fractionalorder systems are studied for the problems of correlated process and measurement noises.The Gr ¨unwald-Letnikov difference method is used to discretize equations with fractional-order nonlinear systems and obtains the difference equations of the systems.In this paper,the unscented Kalman filter algorithm of the fractional-order systems is proposed and achieves state estimation of non-differentiable functions in nonlinear fractional-order systems with correlated noises.Besides,considering the computational load of the actual systems,a finite truncation of the state and input history information are performed.(4)For the problems of correlated processes and measurement noises,the hybrid extendedunscented Kalman filter design problem for continuous-time nonlinear fractional-order systems is studied.Discretization of the nonlinear fractional-order systems studied by Gr ¨unwaldLetnikov difference and fractional-order average derivative methods are used.The nonlinear functions in the system description are applied to the extended Kalman filter and the unscented Kalman filter,and the third-order approximations of the nonlinear function is realized.Meanwhile,the hybrid extended-unscented Kalman filter provided can solve the noise problems of nonlinear fractional-order systems and effectively estimate state of charge of lithium-ion battery under fractional-order systems model with the correlated noises.