A Novel Polynomial-Chaos-Based Kalman Filter

Xu, Yijun; Mili, Lamine; Zhao, Junbo

doi:10.1109/lsp.2018.2879453

Cited by 18 publications

(20 citation statements)

References 24 publications

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“…Chaos is a kind of external, complex, and seemingly irregular motion in the deterministic system due to randomness [1]. e sensitivity of the chaotic system to the initial value makes the input changes of the chaotic system be reflected in the output rapidly, so the chaos theory provides a more realistic nonlinear modeling method [2]. Chaos theory has been proved to be of great significance in a series of critical applications [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…Objectives of this study are (1) to show that R io is a chaotic component of soil respiration in arid land and present a theoretical framework for a better understanding of this chaotic component, (2) to interpret the chaotic system on controls of soil respiration and kinetics of the chaotic system, and (3) to reduce the control complexity of this nonlinear chaotic system by introducing a period regulator.…”

Section: Introductionmentioning

confidence: 99%

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Introducing a Chaotic Component in the Control System of Soil Respiration

Wang

Chen

et al. 2020

Complexity

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Chaos theory has been proved to be of great significance in a series of critical applications although, until now, its applications in analyzing soil respiration have not been addressed. This study aims to introduce a chaotic component in the control system of soil respiration and explain control complexity of this nonlinear chaotic system. This also presents a theoretical framework for better understanding chaotic components of soil respiration in arid land. A concept model of processes and mechanisms associated with subterranean CO2 evolution are developed, and dynamics of the chaotic system is characterized as an extended Riccati equation. Controls of soil respiration and kinetics of the chaotic system are interpreted and as a first attempt, control complexity of this nonlinear chaotic system is tackled by introducing a period-regulator in partitioning components of soil respiration.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Introducing a Chaotic Component in the Control System of Soil Respiration

Wang

Chen

et al. 2020

Complexity

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“…In the FHKF, the expected value of a nonlinear function has to be expressed in closed form, which is always not possible for any arbitrary nonlinear function [26, p. 80]. An algorithm based on the second-order polynomial chaos approximation is proposed in [27] and it is named polynomial chaos Kalman filter (PCKF). It uses a set of support points and Hermite polynomial and is much closer, as an algorithm, to the Gauss Hermite filter (GHF) than our filter.…”

Section: Linear Approximation Using Orthogonal Polynomialsmentioning

confidence: 99%

Extended Kalman Filter Using Orthogonal Polynomials

2021

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This paper reports a new extended Kalman filter where the underlying nonlinear functions are linearized using a Gaussian orthogonal basis of a weighted L 2 space. As we are interested in computing the states' mean and covariance with respect to Gaussian measure, it would be better to use a linearization, that is optimal with respect to the same measure. The resulting first-order polynomial coefficients are approximately calculated by evaluating the integrals using (i) third-order Taylor series expansion (ii) cubature rule of integration. Compared to direct integration-based filters, the proposed filter is far less susceptible to the accumulation of round-off errors leading to loss of positive definiteness. The proposed algorithms are applied to four nonlinear state estimation problems. We show that our proposed filter consistently outperforms the traditional extended Kalman filter and achieves a competitive accuracy to an integration-based square root filter, at a significantly reduced computing cost.

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“…Associated with this set of state vectors, the underlying PDF of the state can be obtained in a nonparametric manner with the introduction of a kernel density estimator. The Parzen-Rosenblatt method [28] for kernel density estimation then obtains the empirical PDF for the state through (13). Figure 3 illustrates this concept for a single state variable during different conditions of the network and the respective empirical probability distribution function.…”

Section: A State Evolution Concept In Power Systemsmentioning

confidence: 99%

“…This limitation has motivated the development of robust approaches as the H-infinite [11], generalized maximum likelihood [12], polynomial-chaos loss function [13], robust hybrid [14], the least absolute value criterion [15], and the cubature robust [16] approaches. All these estimators are widely applied in the literature, and show good performance when dealing with bad data and non-Gaussian noise.…”

Section: Introductionmentioning

confidence: 99%

Tracking Power System State Evolution with Maximum-correntropy-based Extended Kalman Filter

Massignan

London

Miranda

2020

Journal of Modern Power Systems and Clean Energy

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This paper develops a novel approach to track power system state evolution based on the maximum correntropy criterion, due to its robustness against non-Gaussian errors. It includes the temporal aspects on the estimation process within a maximum-correntropy-based extended Kalman filter (MCEKF), which is able to deal with both nonlinear supervisory control and data acquisition (SCADA) and phasor measurement unit (PMU) measurement models. By representing the behavior of the state variables with a nonparametric model within the kernel density estimation, it is possible to include abrupt state transitions as part of the process noise with non-Gaussian characteristics. Also, a novel strategy to update the size of Parzen windows in the kernel estimation is proposed to suppress the effects of suspect samples. By properly adjusting the kernel bandwidth, the proposed MCEKF keeps its accuracy during sudden load changes and contingencies, or in the presence of bad data. Simulations with IEEE test systems and the Brazilian interconnected system are carried out. The results show that the method deals with non-Gaussian noises in both the process and measurement, and provides accurate estimates of the system state under normal and abnormal conditions.

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A Novel Polynomial-Chaos-Based Kalman Filter

Cited by 18 publications

References 24 publications

Introducing a Chaotic Component in the Control System of Soil Respiration

Introducing a Chaotic Component in the Control System of Soil Respiration

Extended Kalman Filter Using Orthogonal Polynomials

Tracking Power System State Evolution with Maximum-correntropy-based Extended Kalman Filter

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