An adaptive Kalman filter estimating process noise covariance

Optimal recursive estimation for networked descriptor systems with packet dropouts, multiplicative noises and correlated noises

The present manuscript aims at raising awareness of the endless possibilities of fractional calculus applied not only to system identification and control engineering, but also into sensing and filtering domains. The creation of the fractance device has enabled the physical realization of a new array of sensors capable of gathering more information. The same fractional-order electronic component has led to the possibility of exploring analog filtering techniques from a practical perspective, enlarging the horizon to a wider frequency range, with increased robustness to component variation, stability and noise reduction. Furthermore, fractional-order digital filters have developed to provide an alternative solution to higher-order integer-order filters, with increased design flexibility and better performance. The present study is a comprehensive review of the latest advances in fractional-order sensors and filters, with a focus on design methodologies and their real-life applicability reported in the last decade. The potential enhancements brought by the use of fractional calculus have been exploited as well in sensing and filtering techniques. Several extensions of the classical sensing and filtering methods have been proposed to date. The basics of fractional-order filters are reviewed, with a focus on the popular fractional-order Kalman filter, as well as those related to sensing. A detailed presentation of fractional-order filters is included in applications such as data transmission and networking, electrical and chemical engineering, biomedicine and various industrial fields.

https://biblio.ugent.be/publication/8726082/file/8726084.pdf

A Review of Recent Advances in Fractional-Order Sensing and Filtering Techniques.

https://pureadmin.qub.ac.uk/ws/files/132341900/Distributed_Weighted_Fusion_Estimation_elsarticle_R2.pdf

Distributed weighted fusion estimation for uncertain networked systems with transmission time-delay and cross-correlated noises

The fractional-order extended Kalman filter (FEKF) algorithm for a nonlinear fractional-order system perturbed by the colored noise is presented. Firstly, the first-order Taylor expansion is employed to linearize the nonlinear functions in the estimated system. Then, Grunwald–Letnikov difference (GLD) and the concept of fractional-order average derivative (FOAD) are employed to discretize nonlinear fractional-order systems perturbed by colored fractional-order process or measurement noise. An augmented system determined by the state and colored noises is presented to treat colored noises. Hence, the FEKFs using GLD and FOAD are carried out, respectively. By comparing two kinds of Kalman filters, FEKFs using FODA can gain the better effect of filtering for colored process or measurement noise to raise the estimation precision. Finally, we discuss three examples to show the validity of investigated FEKFs.

Extended Kalman filters for nonlinear fractional-order systems perturbed by colored noises.

The fractional order calculus can represent systems with high-order dynamics and complex non-linear phenomena using fewer coefficients. In this study the extended fractional Kalman filter is developed for the class of non-linear discrete-time fractional order systems using observations with multiple delays contaminated by additive white noise. For a wide class of practical applications, the time delay cannot be neglected. In the time delay integer order systems, a common approach is partial differential equation. This method is very difficult to solve. The authors’ approach is applied the reorganised innovation technique. As a result of the reorganised innovation sequence, the Kalman filtering problem with multiple delayed measurements is converted to filter of a delay-free system. In the rest of paper, the covariance matrix of the prediction error of the states is presented in the form of the novel Riccati equations. Finally, the solution of the Kalman filtering problem is obtained by applying the re-organised innovation sequence and Riccati equations. A numerical example is given to illustrate the effectiveness of the proposed scheme.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-smt.2016.0089

State estimation strategy for fractional order systems with noises and multiple time delayed measurements

Fuzzy Kalman-type filter for interval fractional-order systems with finite-step auto-correlated process noises

— For fractional order systems that their measurements have multiple time delay, the discrete time Fractional Kalman Filter (FKF) is developed. Reorganized innovation approach is extended for converting the multiple time delay measurement to delay-free system. Then, the optimal solution is obtained by solving the discrete Riccati equation. A numerical example is given to clarify the efficiency of the proposed scheme.

Kalman filtering for fractional order systems with multiple time delay measurement

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State estimation strategy for fractional order systems with noises and multiple time delayed measurements

Fuzzy Kalman-type filter for interval fractional-order systems with finite-step auto-correlated process noises

Kalman filtering for fractional order systems with multiple time delay measurement