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arXiv · 1203.4049

The geometry of low-rank Kalman filters

Silvere Bonnabel·Rodolphe Sepulchre
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Abstract

An important property of the Kalman filter is that the underlying Riccati flow is a contraction for the natural metric of the cone of symmetric positive definite matrices. The present paper studies the geometry of a low-rank version of the Kalman filter. The underlying Riccati flow evolves on the manifold of fixed rank symmetric positive semidefinite matrices. Contraction properties of the low-rank flow are studied by means of a suitable metric recently introduced by the authors.

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Silvere Bonnabel, Rodolphe Sepulchre. 2012-03-19. The geometry of low-rank Kalman filters. https://arxiv.org/abs/1203.4049

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