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Discrete-Time Kalman Filter Design for Linear Infinite-Dimensional Systems

Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada
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Processes 2019, 7(7), 451; https://doi.org/10.3390/pr7070451
Received: 31 May 2019 / Revised: 9 July 2019 / Accepted: 12 July 2019 / Published: 15 July 2019
(This article belongs to the Special Issue Process Systems Engineering à la Canada)
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Abstract

As the optimal linear filter and estimator, the Kalman filter has been extensively utilized for state estimation and prediction in the realm of lumped parameter systems. However, the dynamics of complex industrial systems often vary in both spatial and temporal domains, which take the forms of partial differential equations (PDEs) and/or delay equations. State estimation for these systems is quite challenging due to the mathematical complexity. This work addresses discrete-time Kalman filter design and realization for linear distributed parameter systems. In particular, the structural- and energy-preserving Crank–Nicolson framework is applied for model time discretization without spatial approximation or model order reduction. In order to ensure the time instance consistency in Kalman filter design, a new discrete model configuration is derived. To verify the feasibility of the proposed design, two widely-used PDEs models are considered, i.e., a pipeline hydraulic model and a 1D boundary damped wave equation. View Full-Text
Keywords: discretization; Kalman filter design; infinite-dimensional system; boundary control; water hammer equation; wave equation discretization; Kalman filter design; infinite-dimensional system; boundary control; water hammer equation; wave equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Xie, J.; Dubljevic, S. Discrete-Time Kalman Filter Design for Linear Infinite-Dimensional Systems. Processes 2019, 7, 451.

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