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.
CITATION STYLE
Bonnabel, S., & Sepulchre, R. (2013). The Geometry of Low-Rank Kalman Filters. In Matrix Information Geometry (pp. 53–68). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-30232-9_3
Mendeley helps you to discover research relevant for your work.