Kalman Filtering over Fading Channels: Zero-One Laws and Almost Sure Stabilities
Abstract
In this paper, we investigate probabilistic stability of Kalman filtering over fading channels modeled by -mixing random processes, where channel fading is allowed to generate non-stationary packet dropouts with temporal and/or spatial correlations. Upper/lower almost sure (a.s.) stabilities and absolutely upper/lower a.s. stabilities are defined for characterizing the sample-path behaviors of the Kalman filtering. We prove that both upper and lower a.s. stabilities follow a zero-one law, i.e., these stabilities must happen with a probability either zero or one, and when the filtering system is one-step observable, the absolutely upper and lower a.s. stabilities can also be interpreted using a zero-one law. We establish general stability conditions for (absolutely) upper and lower a.s. stabilities. In particular, with one-step observability, we show the equivalence between absolutely a.s. stabilities and a.s. ones, and necessary and sufficient conditions in terms of packet arrival rate are derived; for the so-called non-degenerate systems, we also manage to give a necessary and sufficient condition for upper a.s. stability.
Keywords
Cite
@article{arxiv.1412.8105,
title = {Kalman Filtering over Fading Channels: Zero-One Laws and Almost Sure Stabilities},
author = {Junfeng Wu and Guodong Shi and Brian D. O. Anderson and Karl Henrik Johansson},
journal= {arXiv preprint arXiv:1412.8105},
year = {2017}
}