Extended Kalman filter for uninterruptible power supplies applied to non linear loads

Zerouali, S.; Allag, A.; Mimoune, S.M.; Srairi, K.; Hamida, Amel Hadri; Féliachi, Mouloud

doi:10.3233/jae-2007-791

Cited by 5 publications

(3 citation statements)

References 1 publication

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“…The extended Kalman filter, as a nonlinear version of Kalman filter, has been widely preferred for various applications. Many contemporary engineering applications such as satellite orbit control , distributed power generation systems , modern optical devices , robots , or the estimated friction require real‐time filtering with nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

Stojanović

Nedić

2015

Intl J Robust & Nonlinear

102

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SUMMARYThe presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez-Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez-Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez-Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non-Gaussian distributions, is illustrated by intensive simulations.

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Section: Introductionmentioning

confidence: 99%

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

Stojanović

Nedić

2015

Intl J Robust & Nonlinear

102

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“…Because of that, there have been increasing research efforts to improve the Kalman filter in order to overcome the nonlinearities and uncertainties. The extended Kalman filter approach has been traditionally used to recursively estimate the states of a nonlinear system corrupted by noise, which has a Gaussian (normal) distribution [6][7][8][9][10][11][12]. The extended Kalman filter uses local linearization to extend the scope of the Kalman filter to the problem of state estimation of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Joint state and parameter robust estimation of stochastic nonlinear systems

Stojanović

Nedić

2015

Intl J Robust & Nonlinear

104

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SUMMARYSuccessful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez-Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non-Gaussian distributions is illustrated by intensive simulations.

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“…Virtually all atmosphere, ocean, and climate models with sufficiently high resolution are turbulent dynamical systems with multiple spatio-temporal scales. Similarly, many contemporary engineering applications such as satellite orbit control [28,7], distributed power generation systems [48,49] or modern optical devices [42,39] require real-time filtering with nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters

Branicki

Gershgorin

Majda

2012

Journal of Computational Physics

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The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters associated with unresolved or unknown processes in the imperfect model "on the fly" through stochastic parameter estimation is an efficient way to increase filtering skill and model performance. Here, a suite of filters implementing stochastic parameter estimation is examined on a nonlinear, exactly solvable, stochastic test model mimicking turbulent signals in regimes ranging from configurations with strongly intermittent, transient instabilities to laminar behavior. Stochastic Parameterization Extended Kalman Filter (SPEKF) systematically corrects both multiplicative and additive biases in the observed dynamics and it involves exact formulas for propagating the mean and covariance including the unresolved parameters in the test model. The remaining filters use the same nonlinear test model but they introduce additional model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics in the stochastic forecast model. A comprehensive study of filter performance is carried out in the presence of various sources of model error as the observation time and observation noise levels are varied. In particular, regimes of filter divergence for the linear tangent filter are identified. The estimation skill of the unresolved stochastic parameters by various filters is also discussed and it is shown that the linear tangent filter, despite its popularity, is completely unreliable in many dynamical regimes. The results presented here provide useful guidelines for filtering turbulent, high-dimensional, spatially extended systems with significant model errors. They also provide unambiguous benchmarks for the capabilities of linear and nonlinear extended Kalman filters on a stringent, exactly solvable test bed.

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Extended Kalman filter for uninterruptible power supplies applied to non linear loads

Cited by 5 publications

References 1 publication

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

Joint state and parameter robust estimation of stochastic nonlinear systems

Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters

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