{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T21:34:03Z","timestamp":1775079243219,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T00:00:00Z","timestamp":1640217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002367","name":"Chinese Academy of Sciences","doi-asserted-by":"publisher","award":["XAB2018YDYL01, XAB2019A06"],"award-info":[{"award-number":["XAB2018YDYL01, XAB2019A06"]}],"id":[{"id":"10.13039\/501100002367","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12073034"],"award-info":[{"award-number":["12073034"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Nowadays, integrity monitoring (IM) is required for diverse safety-related applications using intelligent transport systems (ITS). To ensure high availability for road transport users for in-lane positioning, a sub-meter horizontal protection level (HPL) is expected, which normally requires a much higher horizontal positioning precision of, e.g., a few centimeters. Precise point positioning-real-time kinematic (PPP-RTK) is a positioning method that could achieve high accuracy without long convergence time and strong dependency on nearby infrastructure. As the first part of a series of papers, this contribution proposes an IM strategy for multi-constellation PPP-RTK positioning based on global navigation satellite system (GNSS) signals. It analytically studies the form of the variance-covariance (V-C) matrix of ionosphere interpolation errors for both accuracy and integrity purposes, which considers the processing noise, the ionosphere activities and the network scale. In addition, this contribution analyzes the impacts of diverse factors on the size and convergence of the HPLs, including the user multipath environment, the ionosphere activity, the network scale and the horizontal probability of misleading information (PMI). It is found that the user multipath environment generally has the largest influence on the size of the converged HPLs, while the ionosphere interpolation and the multipath environments have joint impacts on the convergence of the HPL. Making use of 1 Hz data of Global Positioning System (GPS)\/Galileo\/Beidou Navigation Satellite System (BDS) signals on L1 and L5 frequencies, for small- to mid-scaled networks, under nominal multipath environments and for a horizontal PMI down to 2\u00d710\u22126, the ambiguity-float HPLs can converge to 1.5 m within or around 50 epochs under quiet to medium ionosphere activities. Under nominal multipath conditions for small- to mid-scaled networks, with the partial ambiguity resolution enabled, the HPLs can converge to 0.3 m within 10 epochs even under active ionosphere activities.<\/jats:p>","DOI":"10.3390\/rs14010044","type":"journal-article","created":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T21:40:21Z","timestamp":1640295621000},"page":"44","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Integrity Monitoring of PPP-RTK Positioning; Part I: GNSS-Based IM Procedure"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5688-6937","authenticated-orcid":false,"given":"Kan","family":"Wang","sequence":"first","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7060-4123","authenticated-orcid":false,"given":"Ahmed","family":"El-Mowafy","sequence":"additional","affiliation":[{"name":"School of Earth and Planetary Sciences, Curtin University, Perth, WA 6845, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2883-9281","authenticated-orcid":false,"given":"Weijin","family":"Qin","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Xuhai","family":"Yang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1016\/j.asr.2020.05.026","article-title":"Preliminary performance analysis of a prototype DFMC SBAS service over Australia and Asia-Pacific","volume":"66","author":"Wu","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s00190-021-01474-z","article-title":"SBAS DFMC service for Road Transport: Positioning and integrity monitoring with a new weighting model","volume":"95","author":"Wang","year":"2021","journal-title":"J. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"055102","DOI":"10.1088\/1361-6501\/aa5c66","article-title":"Integrity Monitoring of Vehicle Positioning in Urban Environment Using RTK-GNSS, IMU and Speedometer","volume":"28","author":"Kubo","year":"2017","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, K., El-Mowafy, A., Rizos, C., and Wang, J. (2020). Integrity Monitoring for Horizontal RTK Positioning: New Weighting Model and Overbounding CDF in Open-Sky and Suburban Scenarios. Remote Sens., 12.","DOI":"10.3390\/rs12071173"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4025","DOI":"10.1016\/j.asr.2021.02.032","article-title":"Effect of biases in integrity monitoring for RTK positioning","volume":"67","author":"Wang","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Yu, X., and Gao, J. (2017). Kinematic Precise Point Positioning Using Multi-Constellation Global Navigation Satellite System (GNSS) Observations. Int. J. Geo-Inf., 6.","DOI":"10.3390\/ijgi6010006"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5005","DOI":"10.1029\/96JB03860","article-title":"Precise point positioning for the efficient and robust analysis of GPS data from large networks","volume":"102","author":"Zumberge","year":"1997","journal-title":"J. Geophys. Res."},{"key":"ref_8","unstructured":"W\u00fcbbena, G., Schmitz, M., and Bagge, A. (2005, January 13\u201316). PPP-RTK: Precise point positioning using state-space representation in RTK networks. Proceedings of the 18th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2005), Long Beach, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Psychas, D., and Verhagen, S. (2020). Real-Time PPP-RTK Performance Analysis Using Ionospheric Corrections from Multi-Scale Network Configurations. Sensors, 20.","DOI":"10.3390\/s20113012"},{"key":"ref_10","unstructured":"Blanch, J., Walter, T., Enge, P., Lee, Y., Pervan, B., Rippl, M., and Spletter, A. (2012, January 17\u201321). Advanced RAIM user algorithm description: Integrity support message processing, fault detection, exclusion, and protection level calculation. Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation, Nashville, TN, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1002\/navi.49","article-title":"Optimal positioning for advanced Raim. Navig","volume":"60","author":"Blanch","year":"2013","journal-title":"J. Inst. Navig."},{"key":"ref_12","unstructured":"ARAIM Technical Subgroup (2021, December 16). EU-U.S. Cooperation on Satellite Navigation, Working Group C\u2014ARAIM Technical Subgroup, Milestone 3 Report, Final Version, Available online: https:\/\/www.gps.gov\/policy\/cooperation\/europe\/2016\/working-group-c\/."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2148","DOI":"10.1016\/j.asr.2017.01.037","article-title":"Advanced Receiver Autonomous Integrity Monitoring Using Triple Frequency Data with a Focus on Treatment of Biases","volume":"59","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1016\/j.asr.2015.10.046","article-title":"Limited Sensitivity Analysis of ARAIM Availability for LPV-200 over Australia using real data","volume":"57","author":"Yang","year":"2016","journal-title":"Adv. Space Res."},{"key":"ref_15","unstructured":"European Organisation for Civil Aviation Equipment (EUROCAE) (2019). Minimum Operational Performance Standard for Galileo\/Global Positioning System\/Satellite-Based Augmentation System Airborne Equipment, EUROCAE. EUROCAE ED 259."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/10095020.2013.817111","article-title":"Integrity monitoring of fixed ambiguity Precise Point Positioning (PPP) solutions","volume":"16","author":"Jokinen","year":"2013","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gunning, K., Blanch, J., Walter, T., de Groot, L., and Norman, L. (2018, January 24\u201328). Design and Evaluation of Integrity Algorithms for PPP in Kinematic Applications. Proceedings of the 31th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2018), Miami, FL, USA.","DOI":"10.33012\/2018.15972"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1186\/s43020-020-00034-8","article-title":"Vulnerabilities and integrity of precise point positioning for intelligent transport systems: Overview and analysis","volume":"2","author":"Du","year":"2021","journal-title":"Satell. Navig."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s10291-019-0863-x","article-title":"On the detectability of mis-modeled biases in the network-derived positioning corrections and their user impact","volume":"23","author":"Khodabandeh","year":"2019","journal-title":"GPS Solut."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s00190-015-0854-9","article-title":"On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory","volume":"90","author":"Odijk","year":"2015","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1016\/j.asr.2017.06.043","article-title":"A study on predicting network corrections in PPP-RTK processing","volume":"60","author":"Wang","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Baarda, W. (1981). S-transformations and criterion matrices. Publications on Geodesy, Netherlands Geodetic Commission. [2nd ed.]. No. 1.","DOI":"10.54419\/r87y08"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Teunissen, P.J.G. (1985). Zero Order Design: Generalized inverses, adjustment, the datum problem and S-transformations. Optimization and Design of Geodetic Networks, Springer.","DOI":"10.1007\/978-3-642-70659-2_3"},{"key":"ref_24","unstructured":"Ifadis, I.I. (1986). The Atmospheric Delay of Radio Waves: Modelling the Elevation Dependence on a Global Scale, Chalmers University of Technology. Technical Report No. 38L."},{"key":"ref_25","unstructured":"Teunissen, P.J.G. (1993). Least-Squares Estimation of the Integer GPS Ambiguities. Invited Lecture, Section IV Theory and Methodology, Proceedings of the General Meeting of the International Association of Geodesy (IAG), Beijing, China, 8\u201313 August 1993, International Association of Geodesy."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00863419","article-title":"The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation","volume":"70","author":"Teunissen","year":"1995","journal-title":"J. Geod."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.asr.2015.09.002","article-title":"Partial Ambiguity Resolution for Ground and Space-Based Applications in a GPS + Galileo scenario: A simulation study","volume":"57","author":"Nardo","year":"2016","journal-title":"Adv. Space Res."},{"key":"ref_28","unstructured":"Leick, A. (2004). GPS Satellite Surveying, John Wiley and Sons. [3rd ed.]."},{"key":"ref_29","unstructured":"Teunissen, P.J.G., and Verhagen, S. (2004, January 21\u201324). On the Foundation of the Popular Ratio Test for GNSS Ambiguity Resolution. Proceedings of the 17th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2004), Long Beach, CA, USA."},{"key":"ref_30","first-page":"277","article-title":"Comparison of interpolation algorithms in network-based GPS techniques","volume":"2003","author":"Dai","year":"2014","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1029\/RG016i003p00421","article-title":"Least-squares collocation","volume":"16","author":"Moritz","year":"1978","journal-title":"Rev. Geophys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s00190-013-0623-6","article-title":"BLUE, BLUP and the Kalman filter: Some new results","volume":"87","author":"Teunissen","year":"2013","journal-title":"J. Geod."},{"key":"ref_33","unstructured":"Moritz, H. (1976). Covariance Functions in Least-Squares Collocation, The Ohio State University, Department of Geodetic Science. Reports of the Department of Geodetic Science, Report No. 240."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"04018003","DOI":"10.1061\/(ASCE)SU.1943-5428.0000252","article-title":"Satellite-clock modeling in single-frequency PPP-RTK processing","volume":"144","author":"Wang","year":"2018","journal-title":"J. Surv. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1007\/s00190-015-0838-9","article-title":"An analytical study of PPP-RTK corrections: Precision, correlation and user-impact","volume":"89","author":"Khodabandeh","year":"2015","journal-title":"J. Geod."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/TAES.2006.314579","article-title":"Paired overbounding for nonideal LAAS and WAAS error distributions","volume":"42","author":"Rife","year":"2006","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1109\/TAES.2018.2876583","article-title":"Gaussian bounds of sample distributions for integrity analysis","volume":"55","author":"Blanch","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1007\/BF00806368","article-title":"On optimal filtering of GPS dual frequency observations without using orbit information","volume":"65","author":"Euler","year":"1991","journal-title":"Bulletin G\u00e9od\u00e9sique"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/978-3-642-22078-4_24","article-title":"Next generation GNSS single receiver cycle slip reliability","volume":"Volume 137","author":"Sneeuw","year":"2012","journal-title":"VII Hotine-Marussi Symposium on Mathematical Geodesy"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1179\/1752270614Y.0000000100","article-title":"Estimation of multi-constellation GNSS observation stochastic properties using single receiver single satellite data validation method","volume":"47","year":"2015","journal-title":"Surv. Rev."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Odijk, D., and Verhagen, S. (2007, January 14\u201316). Recursive Detection, Identi_cation and Adaptation of Model Errors for Reliable High-Precision GNSS Positioning and Attitude Determination. Proceedings of the 3rd International Conference on Recent Advances in Space Technologies, Istanbul, Turkey.","DOI":"10.1109\/RAST.2007.4284068"},{"key":"ref_42","unstructured":"Beutler, G., Ibauer\u0161ima, I., Gurtner, W., Rothacher, M., Schildknecht, T., and Geiger, A. (1988). Atmospheric refraction and other important biases in GPS carrier phase observations. Atmospheric Effects on Geodetic Space Measurements, School of Surveying, University of New South Wales. Monograph 12."},{"key":"ref_43","unstructured":"Dach, R., Lutz, S., Walser, P., and Fridez, P. (2015). Bernese GNSS Software Version 5.2. User Manual, Bern Open Publishing. Astronomical Institute, University of Bern."},{"key":"ref_44","unstructured":"Wang, K., Meindl, M., Geiger, A., Rothacher, M., Scaramuzza, M., Troller, M., and Truffer, P. (2014, January 8\u201312). Assessment of Single-difference Ionospheric Residuals in a Regional Network for GBAS. Proceedings of the 27th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, FL, USA."},{"key":"ref_45","unstructured":"Schaer, S. (1999). Mapping and predicting the Earth\u2019s ionosphere using the Global Positioning System. Geod\u00e4tisch-Geophysikalische Arbeiten in der Schweiz, Schweizerische Geod\u00e4tische Kommission, Institut f\u00fcr Geod\u00e4sie und Photogrammetrie, Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/1\/44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:51:51Z","timestamp":1760169111000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/1\/44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,23]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["rs14010044"],"URL":"https:\/\/doi.org\/10.3390\/rs14010044","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,23]]}}}