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The geometry of low-rank Kalman filters

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arxiv 1203.4049 v2 pith:UTGE76IV submitted 2012-03-19 math.OC cs.SYeess.SY

The geometry of low-rank Kalman filters

classification math.OC cs.SYeess.SY
keywords flowkalmanlow-rankcontractionfiltergeometrymatricesmetric
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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