Deep Reinforcement Learning with Robust Spatial-Temporal Representation for Improving GNSS Positioning Correction

Deep Reinforcement Learning with Robust Spatial-Temporal Representation for Improving GNSS Positioning Correction | 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 Deep Reinforcement Learning with Robust Spatial-Temporal Representation for Improving GNSS Positioning Correction Zhenni Li, Peili Li, Jianhao Tang, Yulong Song, Liji Chen, Yiting Cai, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7221530/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract In complex urban environments, where GNSS positioning is severely degraded by multipath interference and non-line-of-sight reception, data-driven methods offer a promising solution by effectively modeling complex non-Gaussian errors from sufficient data for positioning correction. The inherent spatial geometric relationships among different constellations in single-epoch GNSS observations, and the temporal dependencies exhibited in sequential multi-epoch observations, contain rich spatial-temporal information that facilitates the modeling of complex stochastic noise in GNSS measurements. However, the effective extraction and correlation of these multidimensional features from GNSS observation data have not yet been sufficiently explored in existing studies. Moreover, dynamic changes in real-world environments induce data distribution shift between training and testing, requiring generalization capability for the data-driven model in unseen scenarios. In this paper, we propose a novel deep reinforcement learning model with robust spatial-temporal representation (DRL-RSTR) for GNSS positioning correction. The spatial geometric relationships among different constellations is modeled by a graph convolutional network (GCN), and the temporal dependencies of sequential observations are captured by transformer. Then, the spatial-temporal features are fused through summation, and a cross-attention network is employed to model the interactions among multi-observations to obtain a comprehensive environmental representation. Finally, we construct a multi-observation GCN-transformer (MOGT) to encode spatial-temporal representation. Additionally, a self-supervised pretext task (SST) is introduced to improve the robustness of spatial-temporal representation against data distribution shift through consistency regularization across non-augmented and augmented observations. We conduct extensive experiments on the public GSDC and built GZGNSS datasets, results show that DRL-RSTR achieves superior positioning accuracy and generalization compared to the model-based and learning-based state-of-the-art methods, with improvements of 51.2% and 41.4% on the GZGNSS dataset and 6.5% compared with kalman filters on the GSDC dataset in terms of positioning accuracy. GNSS positioning deep reinforcement learning self-supervised learning generalization transformer Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 03 Mar, 2026 Reviews received at journal 27 Feb, 2026 Reviewers agreed at journal 03 Feb, 2026 Reviews received at journal 08 Oct, 2025 Reviewers agreed at journal 10 Sep, 2025 Reviewers invited by journal 10 Sep, 2025 Editor assigned by journal 02 Aug, 2025 Submission checks completed at journal 31 Jul, 2025 First submitted to journal 26 Jul, 2025 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-7221530","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":494827509,"identity":"1ec86166-ec1e-49ce-be57-2cce1e572424","order_by":0,"name":"Zhenni Li","email":"","orcid":"","institution":"Guangdong University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhenni","middleName":"","lastName":"Li","suffix":""},{"id":494827510,"identity":"f5ef739a-0685-41e5-ae29-54cc39d939ab","order_by":1,"name":"Peili Li","email":"data:image/png;base64,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","orcid":"","institution":"Guangdong University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Peili","middleName":"","lastName":"Li","suffix":""},{"id":494827512,"identity":"937b08f1-726a-4a75-9fae-b2b288e81ae6","order_by":2,"name":"Jianhao Tang","email":"","orcid":"","institution":"Guangdong University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Jianhao","middleName":"","lastName":"Tang","suffix":""},{"id":494827514,"identity":"d9633a5b-1995-40c5-a3a7-997ebd301ce6","order_by":3,"name":"Yulong Song","email":"","orcid":"","institution":"Guangzhou Haige Communications Group Incorporated Company","correspondingAuthor":false,"prefix":"","firstName":"Yulong","middleName":"","lastName":"Song","suffix":""},{"id":494827515,"identity":"e76251d4-b930-4e55-a0b3-bf12c710ce82","order_by":4,"name":"Liji Chen","email":"","orcid":"","institution":"Guangdong University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Liji","middleName":"","lastName":"Chen","suffix":""},{"id":494827516,"identity":"7df972e7-8533-40f0-b1e6-a6886bdf9b8f","order_by":5,"name":"Yiting Cai","email":"","orcid":"","institution":"Guangdong University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yiting","middleName":"","lastName":"Cai","suffix":""},{"id":494827517,"identity":"312e6da5-cb65-4c35-bfb3-3377a9920321","order_by":6,"name":"Shengli Xie","email":"","orcid":"","institution":"Ministry of Education","correspondingAuthor":false,"prefix":"","firstName":"Shengli","middleName":"","lastName":"Xie","suffix":""}],"badges":[],"createdAt":"2025-07-26 13:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7221530/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7221530/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88366007,"identity":"56b7417a-d27e-4cab-a5b5-e2bdfa189e08","added_by":"auto","created_at":"2025-08-05 17:30:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1084885,"visible":true,"origin":"","legend":"","description":"","filename":"DeepReinforcementLearningwithRobustSpatialTemporalRepresentationforImprovingGNSSPositioningCorrection.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7221530/v1_covered_cc691718-0ff5-49f0-a473-8056b25eba09.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Deep Reinforcement Learning with Robust Spatial-Temporal Representation for Improving GNSS Positioning Correction","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"gps-solutions","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"gpss","sideBox":"Learn more about [GPS Solutions](http://link.springer.com/journal/10291)","snPcode":"10291","submissionUrl":"https://submission.nature.com/new-submission/10291/3","title":"GPS Solutions","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"GNSS positioning, deep reinforcement learning, self-supervised learning, generalization, transformer","lastPublishedDoi":"10.21203/rs.3.rs-7221530/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7221530/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn complex urban environments, where GNSS positioning is severely degraded by multipath interference and non-line-of-sight reception, data-driven methods offer a promising solution by effectively modeling complex non-Gaussian errors from sufficient data for positioning correction. The inherent spatial geometric relationships among different constellations in single-epoch GNSS observations, and the temporal dependencies exhibited in sequential multi-epoch observations, contain rich spatial-temporal information that facilitates the modeling of complex stochastic noise in GNSS measurements. However, the effective extraction and correlation of these multidimensional features from GNSS observation data have not yet been sufficiently explored in existing studies. Moreover, dynamic changes in real-world environments induce data distribution shift between training and testing, requiring generalization capability for the data-driven model in unseen scenarios. In this paper, we propose a novel deep reinforcement learning model with robust spatial-temporal representation (DRL-RSTR) for GNSS positioning correction. The spatial geometric relationships among different constellations is modeled by a graph convolutional network (GCN), and the temporal dependencies of sequential observations are captured by transformer. Then, the spatial-temporal features are fused through summation, and a cross-attention network is employed to model the interactions among multi-observations to obtain a comprehensive environmental representation. Finally, we construct a multi-observation GCN-transformer (MOGT) to encode spatial-temporal representation. Additionally, a self-supervised pretext task (SST) is introduced to improve the robustness of spatial-temporal representation against data distribution shift through consistency regularization across non-augmented and augmented observations. We conduct extensive experiments on the public GSDC and built GZGNSS datasets, results show that DRL-RSTR achieves superior positioning accuracy and generalization compared to the model-based and learning-based state-of-the-art methods, with improvements of 51.2% and 41.4% on the GZGNSS dataset and 6.5% compared with kalman filters on the GSDC dataset in terms of positioning accuracy.\u003c/p\u003e","manuscriptTitle":"Deep Reinforcement Learning with Robust Spatial-Temporal Representation for Improving GNSS Positioning Correction","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-05 17:06:42","doi":"10.21203/rs.3.rs-7221530/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-03T09:07:28+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-27T14:46:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"251190999844953549450897724403920236288","date":"2026-02-03T11:28:57+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-08T13:20:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"26296097419493421214182021913523840797","date":"2025-09-10T10:28:58+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-10T10:15:47+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-02T19:42:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-31T12:49:21+00:00","index":"","fulltext":""},{"type":"submitted","content":"GPS Solutions","date":"2025-07-26T13:30:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"gps-solutions","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"gpss","sideBox":"Learn more about [GPS Solutions](http://link.springer.com/journal/10291)","snPcode":"10291","submissionUrl":"https://submission.nature.com/new-submission/10291/3","title":"GPS Solutions","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"28428ec4-7a68-4225-a9d9-6e309a266a02","owner":[],"postedDate":"August 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-11T10:57:47+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-05 17:06:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7221530","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7221530","identity":"rs-7221530","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}