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Pré-Publication, Document De Travail Année : 2022

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

Résumé

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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Dates et versions

hal-03665666 , version 1 (12-05-2022)
hal-03665666 , version 2 (03-09-2022)

Identifiants

  • HAL Id : hal-03665666 , version 1

Citer

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