Model prediction of spatial non-cooperative target measurement information based on the Koopman operator

Model prediction of spatial non-cooperative target measurement information based on the Koopman operator | 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 Article Model prediction of spatial non-cooperative target measurement information based on the Koopman operator Xiaohong Zhang, Haiyin Zhou, Bowen Hou, Jiongqi Wang, Jian Peng, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4313303/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 This paper proposes a prediction method for spatial non-cooperative measurement information based on the Koopman operator, aiming at the problem of incomplete or missing measurement information in optical relative navigation. Combining the global linear representation theory of the Koopman operator, the paper first projects the nonlinear measurement model into a Hilbert space using a dimensionality expansion function, and constructs a global linear optical measurement model based on the Koopman operator. Secondly, by using a linear combination of Koopman modes, eigenvalues, and feature functions, the paper achieves global linearization of the measurement model, reducing the loss of nonlinear information. Furthermore, a model algorithm based on the Dynamic Mode Decomposition (DMD) method is designed to approximate the Koopman operator, and the main modes of the operator are used to obtain the phase space topology structure of the model, realizing high-precision prediction of measurement information. Finally, Monte Carlo simulation results show that compared with existing methods, the proposed method improves the accuracy of measurement information prediction by 52.07%, providing an effective solution for high-precision prediction of measurement information for subsequent optical relative navigation targets. Physical sciences/Engineering/Aerospace engineering Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Mathematics and computing/Computational science 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-4313303","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":300137790,"identity":"9f9182f1-0e45-4653-bdff-3ca41f40c9a2","order_by":0,"name":"Xiaohong Zhang","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiaohong","middleName":"","lastName":"Zhang","suffix":""},{"id":300137793,"identity":"905ae670-3881-4a43-a382-9729f042da03","order_by":1,"name":"Haiyin Zhou","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Haiyin","middleName":"","lastName":"Zhou","suffix":""},{"id":300137796,"identity":"bbb633fd-5004-4136-a404-d4d52a072779","order_by":2,"name":"Bowen Hou","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Bowen","middleName":"","lastName":"Hou","suffix":""},{"id":300137799,"identity":"e63c3534-6c10-4afe-993e-6b6d6a46884b","order_by":3,"name":"Jiongqi Wang","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Jiongqi","middleName":"","lastName":"Wang","suffix":""},{"id":300137802,"identity":"881df632-87bc-464d-90e9-a6a4eaa1105d","order_by":4,"name":"Jian Peng","email":"","orcid":"","institution":"Hunan University","correspondingAuthor":false,"prefix":"","firstName":"Jian","middleName":"","lastName":"Peng","suffix":""},{"id":300137804,"identity":"a7751022-9d33-45ec-a5cc-a43bf0b8cbad","order_by":5,"name":"Xuanying Zhou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYBACxgbmhgNAOgHIbP/xwcDGjggtjDAtzAckZxSkJRNlDwNEC1uCNM+HQxAuPsA8I7HxwA8Guzx+iRwDYxuDA8wM7IePbsBrx4zEhoM9DMnFkjNyDJJzDO7wMfCkpd0gpOUAD8OBxA23cwwO5xg8Y2aQ4DEjqOXgH4gWw2YLg8OMDcRoOQyxJS2ZmYEoLT0PGw7LMCQnzpz/+Bhjj0FaMhshvxi2Jx/++IbBLrGf52Abw48/Nnb87IeP4dfSALLqH5IIGz7lICBPSMEoGAWjYBSMAgYAQLZQazZvg7AAAAAASUVORK5CYII=","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":true,"prefix":"","firstName":"Xuanying","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2024-04-23 16:13:59","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4313303/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4313303/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":77965144,"identity":"af01f773-8c76-47be-a954-15c02414376c","added_by":"auto","created_at":"2025-03-07 09:39:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3323407,"visible":true,"origin":"","legend":"","description":"","filename":"ModelpredictionofspatialnoncooperativetargetmeasurementinformationbasedontheKoopmanoperator.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4313303/v1_covered_a53f06b8-f67e-40cb-ada2-bfcd03400a43.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Model prediction of spatial non-cooperative target measurement information based on the Koopman operator","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":"","lastPublishedDoi":"10.21203/rs.3.rs-4313303/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4313303/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper proposes a prediction method for spatial non-cooperative measurement information based on the Koopman operator, aiming at the problem of incomplete or missing measurement information in optical relative navigation. Combining the global linear representation theory of the Koopman operator, the paper first projects the nonlinear measurement model into a Hilbert space using a dimensionality expansion function, and constructs a global linear optical measurement model based on the Koopman operator. Secondly, by using a linear combination of Koopman modes, eigenvalues, and feature functions, the paper achieves global linearization of the measurement model, reducing the loss of nonlinear information. Furthermore, a model algorithm based on the Dynamic Mode Decomposition (DMD) method is designed to approximate the Koopman operator, and the main modes of the operator are used to obtain the phase space topology structure of the model, realizing high-precision prediction of measurement information. 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