  Convergence of the Kalman filter is best analyzed by studying the contraction
of the Riccati map in the space of positive definite (covariance) matrices. In
this paper, we explore how this contraction property relates to a more
fundamental non-expansiveness property of filtering maps in the space of
probability distributions endowed with the Hilbert metric. This is viewed as a
preliminary step towards improving the convergence analysis of filtering
algorithms over general graphical models.
