Localization in a wireless sensor network with a geometric approach of Trilateration and mathematical modeling of sine and cosine functions

Localization in a wireless sensor network with a geometric approach of Trilateration and mathematical modeling of sine and cosine functions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Localization in a wireless sensor network with a geometric approach of Trilateration and mathematical modeling of sine and cosine functions Raheleh Ghadami This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3843669/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Wireless sensor network (WSN) has several applications in agriculture, military, rescue, and environmental applications. In a WSN, a large number of sensor nodes are scattered in an operating environment and gather environmental information. The data collected by the WSN is sent to an application in the cloud computing layer or base station for analysis. Gathering information without having their localization and position is not of high value, and accurate localization and position determination of sensor nodes are required in various applications. One method for localization is to use a Global Positioning System (GPS) and install it on all sensor nodes. localization with GPS costs a lot, and on the other hand, this method consumes a lot of energy for localization. DV-Hop technique is a practical method for positioning by reducing the positioning cost. The challenge of the DV-Hop approach for localization is the significant error in locating sensor nodes without a GPS. In this article, a practical localization method is presented by combining the DV-Hop method and the geometric localization method of three references. In this study, the sensor nodes first estimate their distance from the three guide nodes with the step measurement algorithm and then locate them using the Trilateration method. In the proposed approach, the sine and cosine optimization algorithm (SCA) are applied to minimize the positioning error. The evaluations illustrate that the localization error of the suggested approach is lower than the DV-Hop approach. The proposed positioning algorithm has less positioning error than the whale optimization algorithm (WOA), the Harris Hawk Optimization (HHO) algorithm, and the Jellyfish Search optimizer (JSO). The evaluations show that the proposed method of advanced localization methods based on steps such as GSDV-Hop and MGDV-Hop has fewer errors in localization. Wireless Sensor Network (WSN) Geometric Localization Sine and cosine Optimization algorithm (SCA) Global Positioning System (GPS) Mathematical localization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3843669","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":265906506,"identity":"f5e22c57-a96c-4d79-888f-df22745152b2","order_by":0,"name":"Raheleh Ghadami","email":"data:image/png;base64,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","orcid":"","institution":"Istanbul Topkapi University","correspondingAuthor":true,"prefix":"","firstName":"Raheleh","middleName":"","lastName":"Ghadami","suffix":""}],"badges":[],"createdAt":"2024-01-07 21:44:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3843669/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3843669/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50496255,"identity":"c35439e8-74a1-4cb6-8363-32ac120ee552","added_by":"auto","created_at":"2024-02-01 11:52:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":626053,"visible":true,"origin":"","legend":"","description":"","filename":"Art2SinCosinVersion2final.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3843669/v1_covered_162f6643-a228-4630-b7d4-b88772f41782.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Localization in a wireless sensor network with a geometric approach of Trilateration and mathematical modeling of sine and cosine functions","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Wireless Sensor Network (WSN), Geometric Localization, Sine and cosine Optimization algorithm (SCA), Global Positioning System (GPS), Mathematical localization","lastPublishedDoi":"10.21203/rs.3.rs-3843669/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3843669/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWireless sensor network (WSN) has several applications in agriculture, military, rescue, and environmental applications. 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