On the Projective Geometry of Kalman Filter
This work addresses convergence analysis for filtering algorithms, particularly in graphical models, but appears incremental as it builds on existing Kalman filter theory.
The paper tackles the problem of analyzing Kalman filter convergence by relating the contraction of the Riccati map to a non-expansiveness property in probability distributions with the Hilbert metric, aiming to improve convergence analysis for filtering algorithms over graphical models.
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.