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Distributed estimation from relative measurements of heterogeneous and uncertain quality
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 to 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 (ML) estimates and we design two
novel algorithms, based on Least Squares 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 of both algorithms and we
present numerical experiments to evaluate and compare their performance with
classical solutions. 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.Comment: Submitted to IEEE transaction
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