2013
DOI: 10.1063/1.4826062
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A Kalman filtering approach for validation of sensor networks monitoring distributed parameter systems

Abstract: The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type. At a first stage, a nonlinear filtering approach for estimating the dynamics of a 1D nonlinear wave equation, from measurements provided from a small number of sensors is developed. It is shown that the numerical solution of the associated partial differential equation resul… Show more

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Cited by 4 publications
(4 citation statements)
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“…Guo and his co-workers investigated output feedback stabilization and disturbance rejection control of the 1D anti-stable wave equation with [65,66]. In [67], a derivative-free nonlinear Kalman filter was designed for state estimation and fault diagnosis in distributed parameter systems. However, an early lumping method was utilized in the study with spatial order reduction, leading to a spatial approximation design.…”
Section: Introductionmentioning
confidence: 99%
“…Guo and his co-workers investigated output feedback stabilization and disturbance rejection control of the 1D anti-stable wave equation with [65,66]. In [67], a derivative-free nonlinear Kalman filter was designed for state estimation and fault diagnosis in distributed parameter systems. However, an early lumping method was utilized in the study with spatial order reduction, leading to a spatial approximation design.…”
Section: Introductionmentioning
confidence: 99%
“…The transformation is shown to be based on differential flatness theory [12][13][14][15]. The method finally provides a model of the option price dynamics for which state estimation is possible by applying the standard Kalman Filter recursion [16][17][18]. The application of the proposed filtering method is computationally efficient and fast.…”
Section: Introductionmentioning
confidence: 99%
“…This relationship is given from the scalar version of (20) where A and B are n×n matrices. It noted that if A = B with A = aa T , where a is a n×1 vector, then Eq.…”
Section: χ 2 Random Variablesmentioning
confidence: 99%
“…This method, first appearing in [15], has been successfully tested in a wide range of fault diagnosis problems as shown in [16][17][18], while some of its recent applications in nonlinear and distributed parameter systems can be found in [19,20]. Here, the local statistical approach is used to check whether the models of the local Kalman filters that constitute the fuzzy Kalman filter remain consistent with respect to parameters of the real system.…”
Section: Introductionmentioning
confidence: 99%