The geometry of low-rank Kalman filters
Optimization and Control
2013-08-13 v2 Systems and Control
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.
Cite
@article{arxiv.1203.4049,
title = {The geometry of low-rank Kalman filters},
author = {Silvere Bonnabel and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1203.4049},
year = {2013}
}
Comments
Final version published in Matrix Information Geometry, pp53-68, Springer Verlag, 2012