Distributed Estimation from Relative Measurements of Heterogeneous and Uncertain Quality

Chiara Ravazzi*, Nelson P.K. Chan, Paolo Frasca

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    5 Citations (Scopus)

    Abstract

    This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated with nodes connected by an edge. In order to model heterogeneity and uncertainty of the measurements, we assume them to be affected by additive noise distributed according to a Gaussian mixture. In this original setup, we formulate the problem of computing the maximum-likelihood estimates and we design two novel algorithms, based on least squares (LS) regression and expectation maximization (EM). The first algorithm (LS-EM) is centralized and performs the estimation from relative measurements, the soft classification of the measurements, and the estimation of the noise parameters. The second algorithm (Distributed LS-EM) is distributed and performs estimation and soft classification of the measurements, but requires the knowledge of the noise parameters. We provide rigorous proofs of convergence for both algorithms and we present numerical experiments to evaluate their performance and compare it with solutions from the literature. The experiments show the robustness of the proposed methods against different kinds of noise and, for the Distributed LS-EM, against errors in the knowledge of noise parameters.

    Original languageEnglish
    Article number8456538
    Pages (from-to)203-217
    Number of pages15
    JournalIEEE Transactions on Signal and Information Processing over Networks
    Volume5
    Issue number2
    DOIs
    Publication statusPublished - Jun 2019

    Keywords

    • Classification
    • estimation theory
    • Gaussian mixture models
    • maximum-likelihood estimation
    • sensor networks

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