Decentralized Kalman filter comparison for distributed-parameter systems: A case study for a 1D heat conduction process

Hidayat, Zulkifli; Babuška, Robert; Schutter, Bart De; Núñez, Alfredo

doi:10.1109/etfa.2011.6059054

Cited by 25 publications

(11 citation statements)

References 14 publications

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“…Previous approaches to the problem of state estimation for distributed parameter systems, that is for systems described by partial differential equations, can be found in [22][23][24][25][26][27]. The problem treated here is more complicated because the dynamic model of the options' price is no longer described by Black-Scholes PDE, but it also takes into account jump diffusions which finally lead to the form of the partial integrodifferential equation described in Eq.…”

Section: A State Estimation With the Derivative-free Nonlinear Kalmamentioning

confidence: 99%

A Kalman filtering approach to the detection of option mispricing in electric power markets

Rigatos

2014

2014 IEEE Symposium on Computational Intelligence Applications in Smart Grid (CIASG)

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Option pricing models are usually described with the use of stochastic differential equations and diffusion-type partial differential equations (e.g. Black-Scholes models). In case of electric power markets these models are complemented with integral terms which describe the effects of jumps and changes in the diffusion process and which are associated with variations in the production rates, condition of the transmission and distribution system, pay-off capability, etc. Considering the latter case, that is a partial integrodifferential equation for the option's price, a new filtering method is developed for estimating option prices variations without knowledge of initial conditions. The proposed filtering method is the so-called Derivative-free nonlinear Kalman Filter and is based on a transformation of the initial option price dynamics into a state-space model of the linear canonical form. The transformation is shown to be in accordance to differential flatness theory and finally provides a model of the option price dynamics for which state estimation is possible by applying the standard Kalman Filter recursion. Based on the provided state estimate, validation of the Black-Scholes partial integrodifferential equation can be performed and the existence of inconsistent parameters in the electricity market pricing model can be concluded.

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Section: A State Estimation With the Derivative-free Nonlinear Kalmamentioning

confidence: 99%

A Kalman filtering approach to the detection of option mispricing in electric power markets

Rigatos

2014

2014 IEEE Symposium on Computational Intelligence Applications in Smart Grid (CIASG)

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“…The proposed filtering scheme was tested in estimation and fault diagnosis for a wave equation of the form of Eq. (7) under unknown boundary conditions. Nonlinear 1D wave-type partial differential equations of this type appear in models of coupled oscillators.…”

Section: A Detection Of Faulty Sensor Nodesmentioning

confidence: 99%

A Kalman filtering approach for validation of sensor networks monitoring distributed parameter systems

Rigatos¹

2013

AIP Conference Proceedings

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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 results into a set of nonlinear ordinary differential equations. With the application of diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system is obtained in the linear canonical (Brunovsky) form. This transformation enables to obtain local estimates about the state vector of the system through the application of the standard Kalman Filter recursion. At a second stage, the local statistical approach to fault diagnosis is used to perform fault diagnosis for the distributed parameters system by processing with elaborated statistical tools the differences (residuals) between the output of the Kalman Filter and the measurements obtained from the distributed parameter system. Optimal selection of the fault threshold is succeeded by using the local statistical approach to fault diagnosis. The efficiency of the proposed filtering approach for performing fault diagnosis in distributed parameters systems is confirmed through simulation experiments.Index Terms-distributed parameter systems, differential flatness theory, derivative-free nonlinear Kalman Filtering, nonlinear wave equations, local statistical approach to fault diagnosis, fault detection, fault isolation.

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“…The attempts to decentralize and perform distributed Kalman filtering for sensor networks using consensus algorithms are given in [17] and [18]. The comparison of different decentralised KF schemes, including the distributed KF in [17], were conducted in [19] for solving one dimensional linear heat conduction processes. The local estimates of the distributed KF, for time-invariant process and observation models, have been shown to converge to those of the centralised KF (full filter) with the cost of temporarily sacrificing optimality [20] (i.e.…”

Section: Introductionmentioning

confidence: 99%

Switching and information exchange in compressed estimation of coupled high dimensional processes

Narula

Guivant

2019

Automatica

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Compressed Estimation approaches, such as the Generalised Compressed Kalman Filter (GCKF), reduce the computational cost and complexity of high dimensional and high frequency data assimilation problems; usually without sacrificing optimality. Configured using adequate cores, such as the Unscented Kalman Filter (UKF), the GCKF could also treat certain non-linear cases. However, the application of a compressed estimation process is limited to a class of problems which inherently allow the estimation process to be divided, at certain intervals of time, in a subset of lower dimensional problems. This limitation prohibits applying the compressing techniques for estimating densely coupled high dimensional processes. However, those limitations can be overcome by applying proper techniques. In this paper, the concept of subsystem switching, and information exchange architecture, namely 'Exploiting Local Statistical Dependency' (ELSD), has been derived and explored, for allowing compressed estimators to mimic optimal full Gaussian estimators. The performances of the methods have been verified through its application in solving usual types of linear Stochastic Partial Differential Equations (SPDEs). The computational advantages of using the proposed techniques have also been highlighted with recommendation of its usage over the full filter when dealing with high dimensional and high frequency data assimilation.

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Decentralized Kalman filter comparison for distributed-parameter systems: A case study for a 1D heat conduction process

Cited by 25 publications

References 14 publications

A Kalman filtering approach to the detection of option mispricing in electric power markets

A Kalman filtering approach to the detection of option mispricing in electric power markets

A Kalman filtering approach for validation of sensor networks monitoring distributed parameter systems

Switching and information exchange in compressed estimation of coupled high dimensional processes

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