{"title":"Analyzing errors and uncertainties in measurement problems","authors":"K. Tüting , D. Langemann","doi":"10.1016/j.ifacol.2025.03.054","DOIUrl":null,"url":null,"abstract":"<div><div>A practical measurement always raises the question of how well it reproduces the concept to be quantified. We present a mathematical perspective on the measurement problem by introducing a conceptual framework that allows an analytical discussion of this question. Within this framework, we define the measurement result, the concept to be measured, the epistemic errors and aleatory uncertainties. We discuss the first quantifications inside a measurement procedure by analyzing the mathematical spaces and operators. Finally, we apply our considerations to voltage measurements with sampling oscilloscopes.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"59 1","pages":"Pages 313-318"},"PeriodicalIF":0.0000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IFAC-PapersOnLine","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S240589632500271X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
A practical measurement always raises the question of how well it reproduces the concept to be quantified. We present a mathematical perspective on the measurement problem by introducing a conceptual framework that allows an analytical discussion of this question. Within this framework, we define the measurement result, the concept to be measured, the epistemic errors and aleatory uncertainties. We discuss the first quantifications inside a measurement procedure by analyzing the mathematical spaces and operators. Finally, we apply our considerations to voltage measurements with sampling oscilloscopes.
期刊介绍：
All papers from IFAC meetings are published, in partnership with Elsevier, the IFAC Publisher, in theIFAC-PapersOnLine proceedings series hosted at the ScienceDirect web service. This series includes papers previously published in the IFAC website.The main features of the IFAC-PapersOnLine series are: -Online archive including papers from IFAC Symposia, Congresses, Conferences, and most Workshops. -All papers accepted at the meeting are published in PDF format - searchable and citable. -All papers published on the web site can be cited using the IFAC PapersOnLine ISSN and the individual paper DOI (Digital Object Identifier). The site is Open Access in nature - no charge is made to individuals for reading or downloading. Copyright of all papers belongs to IFAC and must be referenced if derivative journal papers are produced from the conference papers. All papers published in IFAC-PapersOnLine have undergone a peer review selection process according to the IFAC rules.
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