  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.
