{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T21:27:28Z","timestamp":1783632448970,"version":"3.55.0"},"reference-count":23,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2019,8,17]],"date-time":"2019-08-17T00:00:00Z","timestamp":1566000000000},"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>Robust and centimeter-level Real-time Kinematic (RTK)-based Global Navigation Satellite System (GNSS) positioning is of paramount importance for emerging GNSS applications, such as drones and automobile systems. However, the performance of conventional single-rover RTK degrades greatly in urban environments due to signal blockage and strong multipath. The increasing use of multiple-antenna\/rover configurations for attitude determination in the above precise positioning applications, just as well, allows more information involved to improve RTK positioning performance in urban areas. This paper proposes a dual-antenna constraint RTK algorithm, which combines GNSS measurements of both antennas by making use of the geometric constraint between them. By doing this, the reception diversity between two antennas can be taken advantage of to improve the availability and geometric distribution of GNSS satellites, and what is more, the redundant measurements from a second antenna help to weaken the multipath effect on the first antenna. Particularly, an Ambiguity Dilution of Precision (ADOP)-based analysis is carried out to explore the intrinsic model strength for ambiguity resolution (AR) with different kinds of constraints. Based on the results, a Dual-Antenna with baseline VEctor Constraint algorithm (RTK) is developed. The primary advantages of the reported method include: (1) Improved availability and success rate of RTK, even if neither of the two single-antenna receivers can successfully solve the AR problem; and (2) reduced computational burden by adopting the concept of measurement projection. Simulated and real data experiments are performed to demonstrate robustness and precision of the algorithm in GNSS-challenged environments.<\/jats:p>","DOI":"10.3390\/s19163586","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T06:10:14Z","timestamp":1566195014000},"page":"3586","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Precise and Robust RTK-GNSS Positioning in Urban Environments with Dual-Antenna Configuration"],"prefix":"10.3390","volume":"19","author":[{"given":"Peirong","family":"Fan","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Satellite Navigation Center, Haidian District, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenyi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaowei","family":"Cui","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingquan","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, T., Zhang, H., Gao, Z., and Chen, Q. (2018). High-accuracy positioning in urban environments using single-frequency multi-GNSS RTK\/MEMS-IMU integration. Remote Sens., 10.","DOI":"10.3390\/rs10020205"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Teunissen, P.J.G., and Kleusberg, A. (1998). GPS for Geodesy, Springer. [2nd ed.].","DOI":"10.1007\/978-3-642-72011-6"},{"key":"ref_3","unstructured":"Teunissen, P.J.G., and Verhagen, S. (2009). GNSS Carrier Phase Ambiguity Resolution: Challenges and Open Problems. Observing Our Changing Earth, Springer."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TMECH.2011.2161485","article-title":"Driftless 3-D attitude determination and positioning of mobile robots by integration of IMU with two RTK GPSs","volume":"18","author":"Aghili","year":"2013","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_5","unstructured":"Shetty, A., and Grace, X. (2015, January 14\u201318). Vision-aided measurement level integration of multiple GPS receivers for UAVs. Proceedings of the 28th International Technical Meeting of the Satellite Division of the Institute of Navigation, Tampa, FL, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1002\/j.2161-4296.2009.tb00442.x","article-title":"A Low-Cost Tightly Coupled GPS\/INS for Small UAVs Augmented with Multiple GPS Antennas","volume":"56","author":"Hirokawa","year":"2009","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_7","first-page":"565","article-title":"Effective Multipath Mitigation Methods for RTK in Urban Environments","volume":"499","author":"Lin","year":"2018","journal-title":"China Satell. Navig. Conf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1918","DOI":"10.1109\/JPROC.2008.2006099","article-title":"Worldwide vertical guidance of aircraft based on modernized GPS and new integrity augmentations","volume":"96","author":"Walter","year":"2008","journal-title":"Proc. IEEE"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"26212","DOI":"10.3390\/s151026212","article-title":"Real-time single-frequency GPS\/MEMS-IMU attitude determination of lightweight UAVs","volume":"10","author":"Eling","year":"2015","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Aghili, F., and Salerno, A. (2009, January 10\u201315). Attitude determination and localization of mobile robots using two RTK GPSs and IMU. Proceedings of the 2009 IEEE\/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO, USA.","DOI":"10.1109\/IROS.2009.5354770"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Leick, A., Rapoport, L., and Tatarnikov, D. (2015). GPS Satellite Surveyin, John Wiley & Sons.","DOI":"10.1002\/9781119018612"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1061\/(ASCE)SU.1943-5428.0000109","article-title":"Study of reliable rapid and ultrarapid static GNSS surveying for determination of the coordinates of control points in obstructed conditions","volume":"139","year":"2013","journal-title":"J. Surv. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"035002","DOI":"10.1088\/0957-0233\/26\/3\/035002","article-title":"Precise GNSS single epoch positioning with multiple receiver configuration for medium-length baselines: Methodology and performance analysis","volume":"26","author":"Paziewski","year":"2015","journal-title":"Meas. Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Suzuki, T., Takahashi, Y., and Amano, Y. (2016, January 12\u201316). Precise UAV Position and Attitude Estimation by Multiple GNSS Receivers for 3D Mapping. Proceedings of the 29th International Technical Meeting of the Satellite Division of the Institute of Navigation, Portland, OR, USA.","DOI":"10.33012\/2016.14621"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10291-008-0103-2","article-title":"A constrained LAMBDA method for GPS attitude determination","volume":"13","author":"Wang","year":"2009","journal-title":"GPS Solut."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Giorgi, G.P., and Teunissen, J.G. (2010, January 6\u201313). Carrier phase GNSS attitude determination with the multivariate constrained LAMBDA method. Proceedings of the 2010 IEEE Aerospace Conference, Big Sky, MT, USA.","DOI":"10.1109\/AERO.2010.5446910"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, W., Fan, P., Cui, X., Zhao, S., Ma, T., and Lu, M. (2018). A Low-Cost INS-Integratable GNSS Ultra-Short Baseline Attitude Determination System. Sensors, 18.","DOI":"10.3390\/s18072114"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1109\/TGRS.1981.350379","article-title":"Miniature Interferometer Terminals for Earth Surveying: Ambiguity And Multipath with Global Positioning System","volume":"GE-14","author":"Counselman","year":"1981","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","first-page":"573","article-title":"A general stochastic approach to solving problems with hard and soft constraints","volume":"35","author":"Kautz","year":"1996","journal-title":"Satisf. Probl. Theory Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/s001900050119","article-title":"A canonical theory for short GPS baselines. Part IV: Precision versus reliability","volume":"71","author":"Teunissen","year":"1997","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s00190-007-0197-2","article-title":"ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models","volume":"82","author":"Odijk","year":"2008","journal-title":"J. Geod."},{"key":"ref_22","unstructured":"Renga, A., Fasano, G., Simonetti, A., and Accardo, D. (2012, January 19\u201321). Fusion of Multi-Antenna Carrier Phase Differential GPS and Inertial Measurements for Performance Evaluation of High Accuracy Integrated Aircraft Navigation Systems. Proceedings of the AIAA Infotech at Aerospace Conference and Exhibit, Garden Grove, CA, USA."},{"key":"ref_23","unstructured":"Kaplan, E., and Hegarty, C. (2005). Understanding GPS: Principles and Applications, Artech House."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3586\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:11:55Z","timestamp":1760188315000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3586"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,17]]},"references-count":23,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["s19163586"],"URL":"https:\/\/doi.org\/10.3390\/s19163586","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,17]]}}}