On the Projective Geometry of Kalman Filter
Optimization and Control
2018-04-11 v2 Machine Learning
Abstract
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.
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Cite
@article{arxiv.1503.09113,
title = {On the Projective Geometry of Kalman Filter},
author = {Francesca Paola Carli and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1503.09113},
year = {2018}
}
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6 pages