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    Stochastic Average Consensus Filter for Distributed HMM Filtering: Almost Sure Convergence


    Ghasemi, Nader and Dey, Subhrakanti and Baras, John S. (2010) Stochastic Average Consensus Filter for Distributed HMM Filtering: Almost Sure Convergence. IFAC Proceedings Volumes, 43 (19). pp. 335-340. ISSN 1474-6670

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    Abstract

    In this paper, we study almost sure convergence of a dynamic average consensus algorithm which allows distributed computation of the product of n time-varying conditional probability density functions. These density functions (often called as “belief functions”) correspond to the conditional probability of observations given the state of an underlying Markov chain, which is observed by n different nodes within a sensor network. The topology of the sensor network is modeled as an undirected graph. The average consensus algorithm is used to obtain a distributed state estimation scheme for a hidden Markov model (HMM). We use the ordinary differential equation (ODE) technique to analyze the convergence of a stochastic approximation type algorithm for achieving average consensus with a constant step size. It is shown that, for a connected graph, under mild assumptions on the first and second moments of the observation probability densities and a geometric ergodicity condition on an extended Markov chain, the consensus filter state of each individual sensor converges almost surely to the true average of the logarithm of the belief functions of all the sensors. Convergence is proved by using a perturbed stochastic Lyapunov function technique. Numerical results suggest that the distributed estimates of the Markov chain state obtained at the individual sensor nodes based on this consensus algorithm track the centralized state estimate (computed on the basis of having access to the observations of all the nodes) quite well, while more formal results on convergence of the distributed HMM filter to the centralized one are currently under investigation.

    Item Type: Article
    Additional Information: Cite as: Nader Ghasemi, Subhrakanti Dey, John S. Baras, Stochastic Average Consensus Filter for Distributed HMM Filtering: Almost Sure Convergence, IFAC Proceedings Volumes, Volume 43, Issue 19, 2010, Pages 335-340, ISSN 1474-6670, ISBN 9783902661821, https://doi.org/10.3182/20100913-2-FR-4014.00083.
    Keywords: Convergence analysis; stochastic approximation; state estimation; stochastic stability; asymptotic properties;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 14481
    Identification Number: https://doi.org/10.3182/20100913-2-FR-4014.00083
    Depositing User: Subhrakanti Dey
    Date Deposited: 31 May 2021 15:22
    Journal or Publication Title: IFAC Proceedings Volumes
    Publisher: Elsevier
    Refereed: Yes
    URI:

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