Distributed estimation from relative measurements of heterogeneous and uncertain quality
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This paper studies the problem of estimation from relative measurements in a graph, where a vector indexed over the nodes has to be reconstructed from relative pairwise measurements of differences between the values of nodes connected by an edge. In order to model the heterogeneity and uncertainty of the measurements, we assume that measurements are 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 propose two novel Expectation-Maximization (EM) algorithms for its solution. The main difference between the two algorithm is that one of them is distributed and the other is not. The former algorithm is said to be distributed because it allows each node to compute the estimate of its own value by using only information that is directly available at the node itself or from its immediate neighbors. We prove convergence of both algorithms and present numerical simulations to evaluate and compare their performance.
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