# Gossip and Distributed Kalman Filtering: Weak Consensus under Weak Detectability - Computer Science > Information Theory

Abstract: The paper presents the gossip interactive Kalman filter GIKF fordistributed Kalman filtering for networked systems and sensor networks, whereinter-sensor communication and observations occur at the same time-scale. Thecommunication among sensors is random; each sensor occasionally exchanges itsfiltering state information with a neighbor depending on the availability ofthe appropriate network link. We show that under a weak distributeddetectability condition:1. the GIKF error process remains stochastically bounded, irrespective of theinstability properties of the random process dynamics; and2. the network achieves \emph{weak consensus}, i.e., the conditionalestimation error covariance at a uniformly randomly selected sensor convergesin distribution to a unique invariant measure on the space of positivesemi-definite matrices independent of the initial state.To prove these results, we interpret the filtered states estimates and errorcovariances at each node in the GIKF as stochastic particles with localinteractions. We analyze the asymptotic properties of the error process bystudying as a random dynamical system the associated switched random Riccatiequation, the switching being dictated by a non-stationary Markov chain on thenetwork graph.

Author: Soummya Kar, José M. F. Moura

Source: https://arxiv.org/