The geometry of low-rank Kalman filters

Details The geometry of low-rank Kalman filters The geometry of low-rank Kalman filters

2012-03-19

arxiv.org/abs/1203.4049v1

Mathematics

Optimization and Control

Scientific paper

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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