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 effe… Show more
“…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.…”
Section: Resultsmentioning
confidence: 99%
“…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].…”
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.
“…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.…”
Section: Resultsmentioning
confidence: 99%
“…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].…”
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.
“…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].…”
Authentication is an important guarantee for vehicle to everything (V2X) commercial deployment. Currently, V2X security often use identity authentication schemes based on public key infrastructure (PKI). These schemes need to transmit certificates and signatures when sending safety-related information such as basic safety messages (BSMs), which need to occupy extra bandwidth and reduce the available channel capacity. So, V2X communication efficiency will be seriously affected in traffic congestion. In this paper, we propose a V2X authentication model based on physical layer characteristics. Then we use the Kalman filter to refine the iterative model and threshold model. The iterative model mainly realizes the priori and posteriori estimation of the current time based on the physical layer characteristics of the previous time, which provides the basis for the entire authentication process. The threshold model analyzes the mathematical characteristics of the priori estimation, and gives the calculation method of the authentication threshold. Since the conventional Kalman filter can only be used for linear discrete system, we use extended Kalman filter and unscented Kalman filter to extend the characteristics used for authentication to non-linearity. At the same time, iterative model and threshold model are improved according to these two algorithms. In terms of security and performance, we compare the proposed schemes with the conventional V2X authentication scheme and physical layer authentication scheme, and the effects of these schemes are analyzed by experiment. We select three characteristics for simulation: received signal strength indication (RSSI), the distance between the two vehicles, and the relative speed between the two vehicles. Then we analyze the process and effect of these two filters, and the factors that affect the threshold. Through experiments, the proposed authentication schemes can effectively take the responsibility of identity authentication in the V2X environment, and have high security level and low overhead, which can reduce the consumption of communication resources by security.
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Hybrid extended-unscented Kalman filters (HEUKFs) for continuous-time nonlinear fractional-order systems with process and measurement noises are investigated in this paper. The Grünwald-Letnikov difference and the fractional-order average derivative (FOAD) method are adopted to discretize the investigated nonlinear fractional-order system, and the nonlinear functions in the system description are coped with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The first-order Taylor expansion used in the EKF method is performed for the nonlinear function at the current time. Meanwhile, the unscented transformation used in the UKF is also concerned for the nonlinear function at the previous time. By using the HEUKF designed in this paper, the third-order approximations for the nonlinear function can be achieved to enhance the accuracy of state estimation and estimation error matrix. Finally, numerical examples are provided to illustrate the effectiveness of the proposed HEUKF for nonlinear fractional-order systems.
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