Dual Estimation of Fractional Variable Order Based on the Unscented Fractional Order Kalman Filter for Direct and Networked Measurements

Sierociuk, Dominik; Macias, Michał; Malesza, Wiktor; Sarwas, Grzegorz

doi:10.1007/s00034-016-0255-1

Cited by 26 publications

(20 citation statements)

References 24 publications

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“…In fact, the FEKF requires the calculation of Jacobian matrix, which is not always available for some systems. Therefore, the fractional-order unscented Kalman filter (FUKF) has been considered by using unscented transformation (UT) instead of linearization [12], [15]- [17]. In [16], the FUKF algorithm has been provided for a nonlinear fractional-order system with both the process and measurement noises.…”

Section: Introductionmentioning

confidence: 99%

Design of a Robust State Estimator for a Discrete-Time Nonlinear Fractional-Order System With Incomplete Measurements and Stochastic Nonlinearities

Zheng

2020

IEEE Access

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In the application of navigation system, networked system, and manufacturing process, incomplete data is unavoidable, which may reduce the performance and stability of the systems. It is a crucial and challenging task when the nonlinear fractional-order system is under incomplete data. As a kind of incomplete data, missing measurements assume that the missing rates of multiple sensors are independent of each other. In order to provide a more reliable and robust state estimation algorithm, a nonlinear fractional-order Kalman filtering algorithm considering both the missing measurements and stochastic nonlinearities is proposed in this paper. Then, the convergence and stability of the proposed filter are analyzed. In addition, sufficient conditions have been investigated to guarantee the stochastic stability. Finally, the effectiveness of the state estimator is verified by two numerical examples.

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Section: Introductionmentioning

confidence: 99%

Design of a Robust State Estimator for a Discrete-Time Nonlinear Fractional-Order System With Incomplete Measurements and Stochastic Nonlinearities

Zheng

2020

IEEE Access

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“…Similarly, this idea can also be extended to nonlinear fractional-order systems. In [24,25], the design method of fractional-order unscented Kalman filter for nonlinear discrete-time fractional-order systems was studied, compared with the fractional-order extended Kalman filter proposed in [18], and fractional-order unscented Kalman filter improves the accuracy of the state estimation [26]. In [27], according to the fractional-order discretization method based on G-L definition and the discrete-time fractional-order system Kalman filter, the robust state estimation of a continuous-time fractional-order system was realized.…”

Section: Introductionmentioning

confidence: 99%

“…The unscented Kalman filters discussed in [24][25][26]28] were performed for nonlinear discrete-time fractional-order systems, but the effect of unscented Kalman filters on the approximation of nonlinear functions were not analyzed. Therefore, this paper uses G-L to discretize the nonlinear continuous-time fractional order system.…”

Section: Introductionmentioning

confidence: 99%

Unscented Kalman filter for continuous‐time nonlinear fractional‐order systems with process and measurement noises

Gao

Liu

Yang

et al. 2019

Asian Journal of Control

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This study proposes the design of unscented Kalman filter for a continuous‐time nonlinear fractional‐order system involving the process noise and the measurement noise. The nonlinear fractional‐order system is discretized to get the difference equation. According to the unscented transformation, the design method of unscented Kalman filter for a continuous‐time nonlinear fractional‐order system is provided. Compared with the extended Kalman filter, the proposed method can obtain a more accurate estimation effect. For fractional‐order systems containing non‐differentiable nonlinear functions, the method proposed in this paper is still effective. The unknown parameters are also discussed by the augmented vector method to achieve the state estimation and parameter identification. Finally, two examples are offered to verify the effectiveness of the proposed unscented Kalman filter for nonlinear fractional‐order systems.

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“…However, as shown in (12), the fractional orders cannot be included directly into the transition function, and thus, the corresponding estimator should be specially designed [38]. The unscented fractional Kalman filter for variable order estimation can be depicted as follows.…”

Section: Fractional Order Estimation Using a Dual Filtermentioning

confidence: 99%

“…For the case of variable orders, there are several ways to extend this definition. In this paper, the A-type variable-order FOC in [38] is adopted due to its simplicity and is defined as:…”

Section: Fractional Order Calculus and Fractional Battery Modelmentioning

confidence: 99%

Battery State-Of-Charge Estimation Based on a Dual Unscented Kalman Filter and Fractional Variable-Order Model

2017

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State-of-charge (SOC) estimation is essential for the safe and effective utilization of lithium-ion batteries. As the SOC cannot be directly measured by sensors, an accurate battery model and a corresponding estimation method is needed. Compared with electrochemical models, the equivalent circuit models are widely used due to their simplicity and feasibility. However, such integer order-based models are not sufficient to simulate the key behavior of the battery, and therefore, their accuracy is limited. In this paper, a new model with fractional order elements is presented. The fractional order values are adaptively updated over time. For battery SOC estimation, an unscented fractional Kalman filter (UFKF) is employed based on the proposed model. Furthermore, a dual estimation scheme is designed to estimate the variable orders simultaneously. The accuracy of the proposed model is verified under different dynamic profiles, and the experimental results indicate the stability and accuracy of the estimation method.

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Dual Estimation of Fractional Variable Order Based on the Unscented Fractional Order Kalman Filter for Direct and Networked Measurements

Cited by 26 publications

References 24 publications

Design of a Robust State Estimator for a Discrete-Time Nonlinear Fractional-Order System With Incomplete Measurements and Stochastic Nonlinearities

Design of a Robust State Estimator for a Discrete-Time Nonlinear Fractional-Order System With Incomplete Measurements and Stochastic Nonlinearities

Unscented Kalman filter for continuous‐time nonlinear fractional‐order systems with process and measurement noises

Battery State-Of-Charge Estimation Based on a Dual Unscented Kalman Filter and Fractional Variable-Order Model

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