Unmodeled-error-corrected long-range ionosphere-free relative positioning with troposphere tomography and particle filter

Unmodeled-error-corrected long-range ionosphere-free relative positioning with troposphere tomography and particle filter | 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 Unmodeled-error-corrected long-range ionosphere-free relative positioning with troposphere tomography and particle filter Zhetao Zhang, Ke Li, Vagner Ferreira, Biyan Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6843068/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 Long-range Real-Time Kinematic (RTK) and Real-Time Differential (RTD) positioning systems face significant challenges from three main types of unmodeled errors: atmospheric delays, multipath effects, and others. This study proposes a comprehensive framework that systematically addresses each error type: first-order ionospheric delays are eliminated using the ionosphere-free combination model; tropospheric delays are corrected through high-resolution troposphere tomography while multipath and other residual unmodeled errors are mitigated using an advanced particle filter algorithm. Specifically, the tropospheric total refractivity field with high spatiotemporal resolutions are tomographically reconstructed with slant tropospheric delays (STDs) from a dense GNSS network. Then the STD for a light-of-sight signal is directly calculated from the tomographic refractivity field and used in the long-range RTK and RTD positioning. In addition, particle filter solves for non-Gaussian and non-stationary unmodeled errors by employing adaptive window dynamic adjustment for covariance and Halton sequence-based low-variance resampling. Experimental results across baselines ranging from 150 km to 600 km demonstrate the superiority of the proposed method, with reductions in root mean square error of up to around 75% in the vertical direction and significant improvements in the horizontal components. These findings highlight the efficacy of combining troposphere tomography and particle filtering to enhance GNSS positioning accuracy, offering a robust solution for high-precision applications in long baselines and even other challenging environments. Long-range RTK/RTD Unmodeled error Troposphere tomography Particle filter 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-6843068","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":524319849,"identity":"44ee78be-6964-4e79-b435-ff3c9c117b30","order_by":0,"name":"Zhetao Zhang","email":"","orcid":"","institution":"Hohai University","correspondingAuthor":false,"prefix":"","firstName":"Zhetao","middleName":"","lastName":"Zhang","suffix":""},{"id":524319850,"identity":"e1920428-bf03-41a7-b32c-14fe4baaf77f","order_by":1,"name":"Ke Li","email":"","orcid":"","institution":"Hohai University","correspondingAuthor":false,"prefix":"","firstName":"Ke","middleName":"","lastName":"Li","suffix":""},{"id":524319851,"identity":"4af05ecb-6931-4bfa-8181-9f8cc9db0bb0","order_by":2,"name":"Vagner Ferreira","email":"","orcid":"","institution":"Hohai University","correspondingAuthor":false,"prefix":"","firstName":"Vagner","middleName":"","lastName":"Ferreira","suffix":""},{"id":524319852,"identity":"a364ff30-7743-43a7-81d4-ee6065c34cd7","order_by":3,"name":"Biyan Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYNACAxtmfgiLmVgtBWnskg2kaflwmN/gALFaDI43P/vMY8AsbXz8+DMJhgrrxAb2swfwazlzzHg2jwGbsdmZHDMJhjPpiQ08eQn4tdxIMGbmMeBJNrvBwybB2HY4sUGCxwC/lvvPPwO1SNRvnsH+TILxHzFabvCAbDFgNpBgMJNgbCBCi+SZnGLGOQYJzBJncowtEo6lG7fx5ODXwnf8+GaGN3/+M/O3H39440ONtWw/+xn8WhQOMDAw8cB4CUDMhlc9EMg3MDAw/iCkahSMglEwCkY2AACmyT/vvIfpUgAAAABJRU5ErkJggg==","orcid":"","institution":"Central South University","correspondingAuthor":true,"prefix":"","firstName":"Biyan","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2025-06-07 13:23:22","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6843068/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6843068/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93179461,"identity":"eb15b04d-ce96-4916-a132-eda95ca1c35d","added_by":"auto","created_at":"2025-10-09 23:34:47","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5956011,"visible":true,"origin":"","legend":"","description":"","filename":"TomographyLongerangeRTKRTDV6.2Jan25ZZT.docx","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/ca7feb74f1625a33b616c946.docx"},{"id":93179373,"identity":"16f2d1c1-76a3-4eb5-acaa-a311c075b26d","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6318,"visible":true,"origin":"","legend":"","description":"","filename":"d1ff3beff5bc4a56af98e712b9f5692d.json","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/cdd62490f6bfafa04d60974a.json"},{"id":93179370,"identity":"64bf3605-7cd2-462e-875b-a5f8a65696d2","added_by":"auto","created_at":"2025-10-09 23:26:47","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":133546,"visible":true,"origin":"","legend":"","description":"","filename":"d1ff3beff5bc4a56af98e712b9f5692d1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/baca9af7589fb2f7cd684db0.xml"},{"id":93179366,"identity":"82932767-3b43-458c-bd8b-6795ca2fec29","added_by":"auto","created_at":"2025-10-09 23:26:47","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":71189,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/0217f4be5dcc90888409c8fa.png"},{"id":93179375,"identity":"0ab09709-2dde-4829-82fc-4164a5016d52","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":101763,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/64da2cde0c607bc166505120.png"},{"id":93179385,"identity":"9441e355-5fa6-41fd-b29a-cded9577e07c","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":101935,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/f316932c87d1e4a171498cc0.png"},{"id":93179379,"identity":"664616ac-c9fd-4fc0-aa13-e597843336e1","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77276,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/368a3ef7c4e382496c8e7ca1.png"},{"id":93179388,"identity":"e5864337-e6b5-4e2e-bad7-07f79aaade05","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":76224,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/63b850c1a5ab5960087e9ae6.png"},{"id":93179381,"identity":"89e11f7d-e356-4660-9ee1-91048ce05947","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":74893,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/6c612b2596ee2811ddab8fd5.png"},{"id":93179374,"identity":"371982ba-73e3-4bf7-afeb-b9bda9f0ca69","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":78207,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/16d5b239c2fc50d49f5ec17e.png"},{"id":93179372,"identity":"0fc73e9d-c38c-40cf-8b3b-a76044cf8c41","added_by":"auto","created_at":"2025-10-09 23:26:47","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77581,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/9b3c098be1f33e6ef5821ee2.png"},{"id":93179392,"identity":"6834a002-3a73-4e1c-a1f8-7ea75548538e","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77538,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/3f2b559034588ab75edb1692.png"},{"id":93179371,"identity":"197a47c5-6e71-4ec6-8d13-93bf6c7750d5","added_by":"auto","created_at":"2025-10-09 23:26:47","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":55861,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/333a097e65c2e5eced743f8b.png"},{"id":93179462,"identity":"0e8e08b6-b6ae-43e8-890b-c97ef679d18c","added_by":"auto","created_at":"2025-10-09 23:34:48","extension":"jpeg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3550489,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/308c1ea85ae6e45b0f59ac51.jpeg"},{"id":93179367,"identity":"aa8e8cc3-6872-49cb-b4d5-84edbf5c0428","added_by":"auto","created_at":"2025-10-09 23:26:47","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":215925,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/7c7118593b82dcdefead30ab.png"},{"id":93179815,"identity":"dbe48713-2030-4866-b592-dbae71c5abc1","added_by":"auto","created_at":"2025-10-09 23:42:48","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":216957,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/12f6e9dea587acce807a1f7d.png"},{"id":93179401,"identity":"c2aea524-45e3-4e69-8bf6-e034a7c37f62","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":231728,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/40636edc786d968ab0cfef52.png"},{"id":93179389,"identity":"14a1bf33-b6d4-4317-b468-88c9cbe5b05c","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":224709,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/07d4ac872a5746001d5b2748.png"},{"id":93179394,"identity":"f5ed67b7-c18d-48d0-a59e-d96e6d03f61b","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":241057,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/4eef4074080155e63a0d7ce7.png"},{"id":93179368,"identity":"a6d57214-fd95-43be-9f63-f172333ba27e","added_by":"auto","created_at":"2025-10-09 23:26:47","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":226746,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/4e8be12fdf10ee362c67c80e.png"},{"id":93179377,"identity":"b3465d17-f633-4e89-862f-e6fe6fad2caa","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":101977,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/f1b6d276990cbe88b5b69e29.png"},{"id":93179467,"identity":"a91acf8a-bc6d-48ce-bb90-5fc7d84808fe","added_by":"auto","created_at":"2025-10-09 23:34:48","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29634,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/a0e6165723e911198931b29e.png"},{"id":93179400,"identity":"668b01f9-491b-418e-97bd-10837fe7ec9e","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":39903,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/2a1e83818438fa7e743f6cf3.png"},{"id":93179391,"identity":"4105a5c2-d0ba-4d55-8377-7d6d99ecb452","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":40161,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/c6763f32f6d304567e910a73.png"},{"id":93179405,"identity":"b3faa9fa-2c15-4f8c-af08-94292f464cf0","added_by":"auto","created_at":"2025-10-09 23:26:49","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":35155,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/38dec0e332ecd36fb083d4b7.png"},{"id":93179384,"identity":"6bbbf5fe-813d-443b-b749-79202840f1c4","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":35310,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/33d79b1492c5630a13940b1e.png"},{"id":93179386,"identity":"1876f4f2-49a5-4f21-bfe8-63ca9decef14","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":34239,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/5c673ea710c90829e803c306.png"},{"id":93179402,"identity":"428dfb9e-9fbd-4ef4-9a3e-b9a2ec0dd176","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":38288,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/09bee648c0aa5b966a9727e8.png"},{"id":93179465,"identity":"cbe495c1-f670-4810-9a0f-09b91aae75cd","added_by":"auto","created_at":"2025-10-09 23:34:48","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":38098,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/8253ca74d0f4e88965de536c.png"},{"id":93179466,"identity":"84e204ca-224f-4e71-a9b2-5ac87e03f8ec","added_by":"auto","created_at":"2025-10-09 23:34:48","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":37077,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/f4e0964a9509638d0f0d878a.png"},{"id":93179397,"identity":"669c9ede-c2b5-4a60-b07e-586f8b58f621","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29235,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/678934773aee63f1a7cb5552.png"},{"id":93179380,"identity":"a1b462b3-0a73-41c9-8b09-d6a0b4103d23","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":200026,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/2cd088b44fa834d13c8bc4aa.png"},{"id":93179403,"identity":"84de2475-3751-4fed-87df-8e4c3439ec73","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":150395,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/2385abfd670b98c3825e3165.png"},{"id":93179404,"identity":"1f892168-81c7-4906-8334-16be5cfc692c","added_by":"auto","created_at":"2025-10-09 23:26:49","extension":"png","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":148881,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/322ed647aecf6e0825cb6803.png"},{"id":93179382,"identity":"d3597524-270a-4ed5-9133-0349fa49c828","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":162271,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/3d5eaef114a75276ace48d59.png"},{"id":93179406,"identity":"a823ec1d-6e7a-4951-8e77-47ca7d76c990","added_by":"auto","created_at":"2025-10-09 23:26:49","extension":"png","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":156654,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/f852bf1c66cf1107946ad14a.png"},{"id":93179387,"identity":"e94f0369-fa91-477b-acd8-71efe95cdecd","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":168535,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/5b499c08b5ef33007774d613.png"},{"id":93179393,"identity":"e1a02c63-1cce-47a7-a000-03864aa8f930","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"png","order_by":37,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":155720,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/a1593a67e4ac33fa838798ac.png"},{"id":93179468,"identity":"0e0da498-048e-4565-a7d2-83aaba0bd2e4","added_by":"auto","created_at":"2025-10-09 23:34:49","extension":"png","order_by":38,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":40119,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/ec611e98df2c08d79e580e1c.png"},{"id":93179396,"identity":"dfa0c2ec-6073-4eb3-aaf8-b6f6ec94dd30","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"xml","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":133152,"visible":true,"origin":"","legend":"","description":"","filename":"d1ff3beff5bc4a56af98e712b9f5692d1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/342e1b4fcf4085355c7a66e5.xml"},{"id":93179383,"identity":"d6c3f474-5ded-4921-a87d-f3aa7398fece","added_by":"auto","created_at":"2025-10-09 23:26:48","extension":"html","order_by":40,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":149998,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1/e67949f50f0e0431d079c55b.html"},{"id":106913103,"identity":"4c92a62e-2790-4168-b1d6-f2b436007c97","added_by":"auto","created_at":"2026-04-14 17:10:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1571582,"visible":true,"origin":"","legend":"","description":"","filename":"TomographyLongerangeRTKRTDV6.2Jan25ZZT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6843068/v1_covered_adad729e-412a-465b-8b0d-154b87834d8e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Unmodeled-error-corrected long-range ionosphere-free relative positioning with troposphere tomography and particle filter","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":"Long-range RTK/RTD, Unmodeled error, Troposphere tomography, Particle filter","lastPublishedDoi":"10.21203/rs.3.rs-6843068/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6843068/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLong-range Real-Time Kinematic (RTK) and Real-Time Differential (RTD) positioning systems face significant challenges from three main types of unmodeled errors: atmospheric delays, multipath effects, and others. This study proposes a comprehensive framework that systematically addresses each error type: first-order ionospheric delays are eliminated using the ionosphere-free combination model; tropospheric delays are corrected through high-resolution troposphere tomography while multipath and other residual unmodeled errors are mitigated using an advanced particle filter algorithm. Specifically, the tropospheric total refractivity field with high spatiotemporal resolutions are tomographically reconstructed with slant tropospheric delays (STDs) from a dense GNSS network. Then the STD for a light-of-sight signal is directly calculated from the tomographic refractivity field and used in the long-range RTK and RTD positioning. In addition, particle filter solves for non-Gaussian and non-stationary unmodeled errors by employing adaptive window dynamic adjustment for covariance and Halton sequence-based low-variance resampling. Experimental results across baselines ranging from 150 km to 600 km demonstrate the superiority of the proposed method, with reductions in root mean square error of up to around 75% in the vertical direction and significant improvements in the horizontal components. These findings highlight the efficacy of combining troposphere tomography and particle filtering to enhance GNSS positioning accuracy, offering a robust solution for high-precision applications in long baselines and even other challenging environments.\u003c/p\u003e","manuscriptTitle":"Unmodeled-error-corrected long-range ionosphere-free relative positioning with troposphere tomography and particle filter","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-09 23:26:42","doi":"10.21203/rs.3.rs-6843068/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"779312a6-b0e7-4159-a2ce-3d9c2f50b07c","owner":[],"postedDate":"October 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-14T17:09:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-09 23:26:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6843068","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6843068","identity":"rs-6843068","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}