2017/10/24 by Chiara Ravazzi, Ravazzi, Chiara, Nelson P. K. Chan +3
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Distributed #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #Parallel #Statistical Methods and Inference #Systems and Control (eess.SY) #and Cluster Computing (cs.DC) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1710.08632
openalex publication_date 2017/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the problem of estimation from relative measurements in a\ngraph, in which a vector indexed over the nodes has to be reconstructed from\npairwise measurements of differences between its components associated to nodes\nconnected by an edge. In order to model heterogeneity and uncertainty of the\nmeasurements, we assume them to be affected by additive noise distributed\naccording to a Gaussian mixture. In this original setup, we formulate the\nproblem of computing the Maximum-Likelihood (ML) estimates and we design two\nnovel algorithms, based on Least Squares regression and\nExpectation-Maximization (EM). The first algorithm (LS- EM) is centralized and\nperforms the estimation from relative measurements, the soft classification of\nthe measurements, and the estimation of the noise parameters. The second\nalgorithm (Distributed LS-EM) is distributed and performs estimation and soft\nclassification of the measurements, but requires the knowledge of the noise\nparameters. We provide rigorous proofs of convergence of both algorithms and we\npresent numerical experiments to evaluate and compare their performance with\nclassical solutions. The experiments show the robustness of the proposed\nmethods against different kinds of noise and, for the Distributed LS-EM,\nagainst errors in the knowledge of noise parameters.\n