{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T16:21:09Z","timestamp":1792599669998,"version":"4.5.0"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,14]],"date-time":"2021-04-14T00:00:00Z","timestamp":1618358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>When applying a diagnostic technique to complex systems, whose dynamics, constraints, and environment evolve over time, being able to re-evaluate the residuals that are capable of detecting defaults and proposing the most appropriate ones can quickly prove to make sense. For this purpose, the concept of adaptive diagnosis is introduced. In this work, the contributions of information theory are investigated in order to propose a Fault-Tolerant multi-sensor data fusion framework. This work is part of studies proposing an architecture combining a stochastic filter for state estimation with a diagnostic layer with the aim of proposing a safe and accurate state estimation from potentially inconsistent or erroneous sensors measurements. From the design of the residuals, using \u03b1-R\u00e9nyi Divergence (\u03b1-RD), to the optimization of the decision threshold, through the establishment of a function that is dedicated to the choice of \u03b1 at each moment, we detail each step of the proposed automated decision-support framework. We also dwell on: (1) the consequences of the degree of freedom provided by this \u03b1 parameter and on (2) the application-dictated policy to design the \u03b1 tuning function playing on the overall performance of the system (detection rate, false alarms, and missed detection rates). Finally, we present a real application case on which this framework has been tested. The problem of multi-sensor localization, integrating sensors whose operating range is variable according to the environment crossed, is a case study to illustrate the contributions of such an approach and show the performance.<\/jats:p>","DOI":"10.3390\/e23040463","type":"journal-article","created":{"date-parts":[[2021,4,14]],"date-time":"2021-04-14T15:30:39Z","timestamp":1618414239000},"page":"463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Adaptive Diagnosis for Fault Tolerant Data Fusion Based on \u03b1-R\u00e9nyi Divergence Strategy for Vehicle Localization"],"prefix":"10.3390","volume":"23","author":[{"given":"Khoder","family":"Makkawi","sequence":"first","affiliation":[{"name":"CRIStAL, Centre de Recherche en Informatique Signal et Automatique de Lille, Universit\u00e9 de Lille, CNRS, UMR 9189, F-59000 Lille, France"},{"name":"Azm Center for Research in Biotechnology and Its Application, EDST, Lebanese University, Tripoli 1300, Lebanon"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nourdine","family":"Ait-Tmazirte","sequence":"additional","affiliation":[{"name":"IFSTTAR, COSYS, LEOST, Universit\u00e9 Gustave Eiffel, F-59650 Villeneuve D\u2019Ascq, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0267-264X","authenticated-orcid":false,"given":"Maan","family":"El Badaoui El Najjar","sequence":"additional","affiliation":[{"name":"CRIStAL, Centre de Recherche en Informatique Signal et Automatique de Lille, Universit\u00e9 de Lille, CNRS, UMR 9189, F-59000 Lille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7129-0848","authenticated-orcid":false,"given":"Nazih","family":"Moubayed","sequence":"additional","affiliation":[{"name":"CRSI LaRGES, Lebanese University, Tripoli 1300, Lebanon"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,14]]},"reference":[{"key":"ref_1","unstructured":"National Highway Traffic Safety Administration (2015). 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