# Kernel representation of Kalman observer and associated $H$-matrix based discretization

2 IDEFIX - Inversion of Differential Equations For Imaging and physiX
Inria Saclay - Ile de France, X - École polytechnique, EDF - EDF
3 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
Abstract : In deterministic estimation, applying a Kalman filter to a dynamical model based on partial differential equations is theoretically seducing but solving the associated Riccati equation leads to a so-called curse of dimensionality for its numerical implementation. In this work, we propose to entirely revisit the theory of Kalman filters for parabolic problems where additional regularity results proves that the Riccati equation solution belongs to the class of Hilbert-Schmidt operators. The regularity of the associated kernel then allows to proceed to the numerical analysis of the Kalman full space-time discretization in adapted norms, hence justifying the implementation of the related Kalman filter numerical algorithm with H-matrices typically developed for integral equations discretization.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03658937
Contributor : Philippe Moireau Connect in order to contact the contributor
Submitted on : Wednesday, May 4, 2022 - 1:26:49 PM
Last modification on : Friday, May 6, 2022 - 3:13:55 AM

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h-matrix-observer-hal.pdf
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• HAL Id : hal-03658937, version 1

### Citation

Matthieu Aussal, Philippe Moireau. Kernel representation of Kalman observer and associated $H$-matrix based discretization. 2022. ⟨hal-03658937⟩

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