Accéder directement au contenu Accéder directement à la navigation
Communication dans un congrès

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 : We consider the filtering problem of estimating the state of a continuous-time dynamical process governed by a nonlinear stochastic differential equation and observed through discrete-time measurements. As the Bayesian posterior density is difficult to compute, we use variational inference (VI) to approximate it. This is achieved by seeking the closest Gaussian density to the posterior, in the sense of the Kullback- Leibler divergence (KL). The obtained algorithm, called the continuous-discrete variational Kalman filter (CD-VKF), provides implicit formulas that solve the considered problem in closed form. Our framework avoids local linearization, and the estimation error is globally controlled at each step. We first clarify the connections between well known nonlinear Kalman filters and VI, then develop closed form approximate formulas for the CD-VKF. Our algorithm achieves state-of-the-art performances on the problem of reentry tracking of a space capsule.
Type de document :
Communication dans un congrès
Liste complète des métadonnées

https://hal.inria.fr/hal-03665666
Contributeur : Marc Lambert Connectez-vous pour contacter le contributeur
Soumis le : samedi 3 septembre 2022 - 18:10:35
Dernière modification le : mercredi 7 septembre 2022 - 03:44:05

Fichier

CD_VKF_HAL-v2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-03665666, version 2

Collections

Citation

Marc Lambert, Silvère Bonnabel, Francis Bach. The continuous-discrete variational Kalman filter (CD-VKF). 61st IEEE Conference on Decision and Control, Dec 2022, Cancun, Mexico. ⟨hal-03665666v2⟩

Partager

Métriques

Consultations de la notice

1027

Téléchargements de fichiers

7991