Full adaptive Kalman filters for nonlinear fractional-order systems containing unknown parameters and fractional-orders

Huang, Xiaomin; Gao, Zhe

doi:10.1177/01423312221086070

Cited by 4 publications

(2 citation statements)

References 36 publications

(35 reference statements)

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“…However, a modified version of the optimal robust filter presented in Reference 49 can be employed to overcome this issue. When the measurement noise covariance matrix

{\mathbf{R}}_k

is positive semi‐definite due to the presence of redundant information, the proposed algorithm may not be applicable, as discussed in Reference 50. However, this issue can be addressed by using the alternative 3‐block representation method, which can handle singular measurement noise covariance. An adaptive version of the designed robust filter can be taken into account by estimating unknown parameters and fractional orders based on the method of augmented vector introduced in Reference 51.…”

Section: Discussionmentioning

confidence: 99%

Robust fractional order singular Kalman filter

Nosrati,

Belikov,

Tepljakov

et al. 2023

Intl J Robust & Nonlinear

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In this article, the state estimation problem of linear fractional order singular (FOS) systems subject to matrix uncertainties is investigated where a recursive robust algorithm is derived. Considering an uncertain discrete‐time linear FOS system with added process and measurement noises, we aim to design a robust Kalman‐type state estimation algorithm based on an optimal data fitting approach with a given sequence of observations. As a substitute for the stochastic formulation, this general filter is obtained by minimizing a completely deterministic regularized residual norm in its worst‐possible form at each step over admissible uncertainties. Analysis of the algorithm shows that not only does the proposed robust filter cover the traditional robust Kalman filters (KFs), but it also represents an extension of the nominal fractional singular KF (FSKF) when the system is not subject to uncertainties. Furthermore, besides giving a sufficient condition for the existence of the robust filter, we derive conditions for the asymptotic properties of the filter, where we demonstrate that the filter and the Riccati equation are stable and converge when an equivalent system is detectable and stabilizable. A numerical example is included to demonstrate the performance of the introduced filter.

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“…However, a modified version of the optimal robust filter presented in Reference 49 can be employed to overcome this issue. When the measurement noise covariance matrix

{\mathbf{R}}_k

Section: Discussionmentioning

confidence: 99%

Robust fractional order singular Kalman filter

Nosrati,

Belikov,

Tepljakov

et al. 2023

Intl J Robust & Nonlinear

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show abstract

“…An adaptive Kalman filtering technique in ref. [37] handled the initial value as a state by augmenting the vector to reduce the effect of the initial value. Based on the above findings, an initial value compensation (IVC) is applied in this study to weaken the effect of initial values on the SOC estimation of LIBs using the augmented vector approach.…”

Section: Introductionmentioning

confidence: 99%

An Initial Value Problem for State of Charge Estimation of Lithium‐Ion Batteries with an Adaptive Fractional‐Order Unscented Particle Filter

Jiao,

Gao,

Chai

et al. 2023

Advcd Theory and Sims

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This paper proposes an adaptive fractional‐order unscented particle filter (AFOUPF) with the initial value compensation (IVC) to enhance the estimation accuracy of the state of charge (SOC) for lithium‐ion batteries (LIBs). First, to correctly reflect the dynamic properties of LIBs, a fractional‐order system (FOS) with a constant phase component is constructed. Second, to discretize the FOS equation of LIBs, the Grünwald–Letnikov difference, Caputo derivative and Rieman–Liouville difference are employed to establish the corresponding difference equation. Third, a map function is applied to keep the order and SOC of the FOS within an appropriate interval. Further, an approach of IVC is provided for the AFOUPF to increase the accuracy of SOC estimation, taking into account that the accuracy of SOC estimation is impacted if the order of the FOS is relatively small in (0, 1). By utilizing the augmented vector approach, the simultaneous estimations of order, parameters, initial value, and SOC are resolved. Besides, an iterative approach that accommodates the noise covariance matrices is proposed to improve the estimation accuracy. The AFOUPF conducts an unscented transform and resampling on each particle, resulting in a high SOC estimation accuracy in complicated situations. Finally, the availability of AFOUPF is tested by several experiments.

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Maximum correntropy smoothers based on information theoretic learning in non-Gaussian environments

Ma,

Liu,

Zhang

et al. 2024

Transactions of the Institute of Measurement and Control

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Non-Gaussian noise processing is difficult in dynamics systems, and smoothing plays an important role for state estimation. As an optimization criterion in information theoretic learning, the maximum correntropy has been recently applied to filtering tasks and achieves decent performance in various non-Gaussian scenarios. In this paper, by using maximum correntropy criterion instead of minimum mean square error criterion, two new smoothers called a fixed-point maximum correntropy smoother and a fixed-lag maximum correntropy smoother are proposed to improve smoothing performance in linear dynamics systems with complex non-Gaussian noise. Similar to the traditional Kalman smoother, the proposed smoothers are also online recursive algorithms, which use propagation equations to update the state estimates and the corresponding covariance matrices. In addition, the computational complexities of the proposed smoothers are analyzed, and their performance is further discussed mathematically using estimate covariance. The simulation results demonstrate that the two proposed maximum correntropy smoothers exhibit superior smoothing performance compared to conventional Kalman smoothers when the underlying system is subjected to non-Gaussian noise, and the best observed improvement in performance is approximately 50% and 80%, respectively.

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Full adaptive Kalman filters for nonlinear fractional-order systems containing unknown parameters and fractional-orders

Cited by 4 publications

References 36 publications

Robust fractional order singular Kalman filter

Robust fractional order singular Kalman filter

An Initial Value Problem for State of Charge Estimation of Lithium‐Ion Batteries with an Adaptive Fractional‐Order Unscented Particle Filter

Maximum correntropy smoothers based on information theoretic learning in non-Gaussian environments

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