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Pré-publication, Document de travail

The continuous-discrete variational Kalman filter (CD-VKF)

Marc Lambert 1, 2 Silvère Bonnabel 3, 4 Francis Bach 2 
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : In this paper we seek to estimate the state of a continuous-time dynamical process governed by a nonlinear stochastic differential equation, observed through discrete-time measurements. As the Bayesian posterior density is difficult to compute, we use variational inference (VI)-a method from machine learning-to approximate it. This is achieved by seeking the closest Gaussian density to the posterior, in the sense of the Kullback-Leibler divergence. The obtained algorithm, called the continuous-discrete variational Kalman filter (CD-VKF), provides implicit formulas that solve the considered problem. Our hope is that such a Kalman filter variant may prove more stable as it optimizes a closeness to the target distribution. We first clarify the connections between many Kalman filter variants and VI, then develop closed form approximate formulas for the CD-VKF. Our algorithm gives state of the art performances on the problem of reentry tracking of a space capsule.
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Pré-publication, Document de travail
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https://hal.inria.fr/hal-03665666
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Soumis le : jeudi 12 mai 2022 - 07:19:28
Dernière modification le : mercredi 7 septembre 2022 - 03:44:05

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CD-VKF.pdf
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  • HAL Id : hal-03665666, version 1

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Marc Lambert, Silvère Bonnabel, Francis Bach. The continuous-discrete variational Kalman filter (CD-VKF). 2022. ⟨hal-03665666v1⟩

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