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

Abstract

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.

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

“…The probability of the measurements missing rates has been used in (23) to compensate the effect of missing measurements. Moreover, the information of the stochastic nonlinearities have been considered in (16) and (25) to improve the estimation performance. From this point of view, the proposed state estimator has certain robustness against the missing measurements and stochastic nonlinearities.…”

“…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. Moreover, considering measurements are sampled through a lossy network, the FUKF has been utilized as a variable order estimation method in [17].…”

Physical Layer Authentication Based on Nonlinear Kalman Filter for V2X Communication

“…Generally, only first-order expansion is performed to reduce the computational complexity [37], [38]. Unscented Kalman filter uses a sampling method to approximate the probability density distribution of nonlinear equations [39], [40], and uses a unscented transformation method to reduce the number of sampling points [41]. With the development of information technology, Kalman filter can be used not only for signal processing, but also for vehicle state estimation [42], [43].…”

Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises

“…For some systems with strong nonlinearity, the estimation effect of the EKF algorithm is not satisfactory. Hence, the UKF was considered to improve the estimation accuracy of fractional-order systems in Gao et al (2019). A method based on fuzzy logic was proposed to improve the fractional-order UKF with the adaptive noise covariance in Ramezani and Safarinejadian (2018), and the convergence and accuracy of the state estimation was improved.…”

“…The main highlights of this paper are summarized as follows: (1) The estimation of nonlinear continuous-time fractional-order system is discretized by fractional-order average derivative in Yang et al (2018) and the Grünwald-Letnikov differential (GLD) definition in Gao et al (2019), and the sampling period is also a parameter of the nonlinear function. The nonlinear difference equation is obtained to reveal the dynamic characteristics.…”