{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T03:00:25Z","timestamp":1777431625324,"version":"3.51.4"},"reference-count":26,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,3]],"date-time":"2018-04-03T00:00:00Z","timestamp":1522713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Precise point positioning (PPP) and its integer ambiguity resolution-enabled variant, PPP-RTK (real-time kinematic), can benefit enormously from the integration of multiple global navigation satellite systems (GNSS). In such a multi-GNSS landscape, the positioning convergence time is expected to be reduced considerably as compared to the one obtained by a single-GNSS setup. It is therefore the goal of the present contribution to provide numerical insights into the role taken by the multi-GNSS integration in delivering fast and high-precision positioning solutions (sub-decimeter and centimeter levels) using PPP-RTK. To that end, we employ the Curtin PPP-RTK platform and process data-sets of GPS, BeiDou Navigation Satellite System (BDS) and Galileo in stand-alone and combined forms. The data-sets are collected by various receiver types, ranging from high-end multi-frequency geodetic receivers to low-cost single-frequency mass-market receivers. The corresponding stations form a large-scale (Australia-wide) network as well as a small-scale network with inter-station distances less than 30 km. In case of the Australia-wide GPS-only ambiguity-float setup, 90% of the horizontal positioning errors (kinematic mode) are shown to become less than five centimeters after 103 min. The stated required time is reduced to 66 min for the corresponding GPS + BDS + Galieo setup. The time is further reduced to 15 min by applying single-receiver ambiguity resolution. The outcomes are supported by the positioning results of the small-scale network.<\/jats:p>","DOI":"10.3390\/s18041078","type":"journal-article","created":{"date-parts":[[2018,4,3]],"date-time":"2018-04-03T13:31:51Z","timestamp":1522762311000},"page":"1078","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":90,"title":["Multi-GNSS PPP-RTK: From Large- to Small-Scale Networks"],"prefix":"10.3390","volume":"18","author":[{"given":"Nandakumaran","family":"Nadarajah","sequence":"first","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5051-8233","authenticated-orcid":false,"given":"Amir","family":"Khodabandeh","sequence":"additional","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5688-6937","authenticated-orcid":false,"given":"Kan","family":"Wang","sequence":"additional","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mazher","family":"Choudhury","sequence":"additional","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4143-6006","authenticated-orcid":false,"given":"Peter","family":"Teunissen","sequence":"additional","affiliation":[{"name":"GNSS Research Centre, Department of Spatial Sciences, Curtin University, Perth, WA 6845, Australia"},{"name":"Department of Geoscience and Remote Sensing, Delft University of Technology, 2628 CN, Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,3]]},"reference":[{"key":"ref_1","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_2","first-page":"223","article-title":"PPP-RTK: Results of CORS Network-Based PPP with Integer Ambiguity Resolution","volume":"42","author":"Teunissen","year":"2010","journal-title":"J. Aeronaut. Astronaut. Aviat."},{"key":"ref_3","first-page":"571","article-title":"Single-Frequency PPP-RTK: Theory and Experimental Results","volume":"Volume 139","author":"Odijk","year":"2014","journal-title":"IAG Symposium Earth on the Edge: Science for a Sustainable Planet"},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1002\/navi.57","article-title":"Global and Regional Ionospheric Corrections for Faster PPP Convergence","volume":"61","author":"Banville","year":"2014","journal-title":"Navigation"},{"key":"ref_6","unstructured":"Leandro, R., Landau, H., Nitschke, M., Glocker, M., Seeger, S., Chen, X., Deking, A., BenTahar, M., Zhang, F., and Ferguson, K. (2011, January 20\u201323). RTX Positioning: The Next Generation of cm-accurate Real-time GNSS Positioning. Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yu, X., and Gao, J. (2017). Kinematic Precise Point Positioning Using Multi-Constellation Global Navigation Satellite System (GNSS) Observations. ISPRS Int. J. Geo-Inf., 6.","DOI":"10.3390\/ijgi6010006"},{"key":"ref_8","unstructured":"Collins, P. (2008, January 28\u201330). Isolating and estimating undifferenced GPS integer ambiguities. Proceedings of the 2008 National Technical Meeting of the Institute of Navigation, San Diego, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00190-007-0187-4","article-title":"Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations","volume":"82","author":"Ge","year":"2008","journal-title":"J. Geodesy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1664","DOI":"10.1016\/j.asr.2010.03.030","article-title":"Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning","volume":"47","author":"Geng","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_11","unstructured":"Laurichesse, D., and Mercier, F. (2007, January 25\u201328). Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. Proceedings of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2007), Fort Worth, TX, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1007\/s00190-012-0559-2","article-title":"Zero-difference GPS ambiguity resolution at CNES\u2013CLS IGS Analysis Center","volume":"86","author":"Loyer","year":"2012","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00190-014-0771-3","article-title":"Review and principles of PPP-RTK methods","volume":"89","author":"Teunissen","year":"2015","journal-title":"J. Geod."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1080\/14498596.2016.1261373","article-title":"PPP-RTK by means of S-system theory: Australian network and user demonstration","volume":"62","author":"Odijk","year":"2017","journal-title":"J. Spat. Sci."},{"key":"ref_15","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_16","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":"2016","journal-title":"J. Geod."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Baarda, W. (1981). S-Transformations and Criterion Matrices, Netherlands Geodetic Commission. [2nd ed.].","DOI":"10.54419\/r87y08"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Grafarend, E.W., and Sans\u00f2, F. (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"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Teunissen, P.J.G., and Montenbruck, O. (2017). Springer Handbook of Global Navigation Satellite Systems, Springer International Publishing.","DOI":"10.1007\/978-3-319-42928-1"},{"key":"ref_20","unstructured":"Schaer, S. (1999). Mapping and Predicting the Earth\u2019s Ionosphere Using the Global Positioning System. [Ph.D. Thesis, University of Bern]."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Odijk, D. (2002). Fast Precise GPS Positioning in the Presence of Ionospheric Delays. [Ph.D. Thesis, Delft University of Technology].","DOI":"10.54419\/hgkyde"},{"key":"ref_22","unstructured":"Multi-GNSS Experiment (MGEX) (2024, June 10). MGEX Orbit Products. NASA CDDIS, Available online: ftp:\/\/cddis.gsfc.nasa.gov\/gnss\/products\/mgex\/."},{"key":"ref_23","first-page":"42","article-title":"IGS-MGEX: Preparing the Ground for Multi-Constellation GNSS Science","volume":"9","author":"Montenbruck","year":"2014","journal-title":"Inside GNSS"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/j.asr.2017.01.011","article-title":"The Multi\u2013GNSS Experiment (MGEX) of the International GNSS Service (IGS)\u2014Achievements, prospects and challenges","volume":"59","author":"Montenbruck","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_25","unstructured":"Teunissen, P.J.G. (1990, January 20). Quality control in integrated navigation systems. Proceedings of the IEEE PLANS\u201990, Position Location and Navigation Symposium, Record, The 1990\u2019s\u2014A Decade of Excellence in the Navigation Sciences, Las Vegas, NV, USA."},{"key":"ref_26","unstructured":"Google Earth (2018). Google Earth Imagery\u201d (November 5, 2017). Google Earth 7.0.3.8542, Google Earth. \u00a9 2018 Google, Data SIO, NOAA, U.S. Navy. NGA. GEBCO."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1078\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:59:30Z","timestamp":1760194770000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,3]]},"references-count":26,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["s18041078"],"URL":"https:\/\/doi.org\/10.3390\/s18041078","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,3]]}}}