{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T00:40:44Z","timestamp":1767832844464,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2021,11,24]],"date-time":"2021-11-24T00:00:00Z","timestamp":1637712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41804028"],"award-info":[{"award-number":["41804028"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41874037"],"award-info":[{"award-number":["41874037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018583","name":"Wuhan science and technology project","doi-asserted-by":"publisher","award":["2018010401011271"],"award-info":[{"award-number":["2018010401011271"]}],"id":[{"id":"10.13039\/501100018583","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Joint Fund of Ministry of Education of China for Equipment Pre-research","award":["6141A02011907"],"award-info":[{"award-number":["6141A02011907"]}]},{"name":"China's major projects of the second generation satellite navigation system","award":["GFZX030302030205-1"],"award-info":[{"award-number":["GFZX030302030205-1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The rapid development of unmanned aerial vehicles (UAVs) in recent years has promoted their application in various fields, such as precise agriculture, formation flight, etc. In these applications, the accurate and reliable real-time position and attitude determination between each moving device in the same platform system are the key issue for safe and effective cooperative works. In traditional ways, static reference stations should be set up near the platform to keep the stable position datum of the platform system. In this paper, we abandoned the static stations and expected to achieve stable position datums with the platform system itself. To achieve this goal, we proposed an improved method based on both the Global Positioning System (GPS)\/Beidou Navigation Satellite System (BDS) data and the inertial navigation system (INS) data to obtain precise positions of the moving devices. The time-differenced carrier phase (TDCP) was used to get the position variations and update the positions over time, and then, the INS data was integrated to further improve the accuracy and reliability of the updated positions; thus, this method is denoted as the TDCP\/INS method. To evaluate the performance of this method and compare it with the traditional single-point positioning (SPP) method and the Kalman filtered SPP (KFSPP) method, a field vehicle experiment was conducted, and the position results achieved from these three methods were compared with those from the tightly combined real-time kinematic positioning (RTK)\/INS method, where centimeter-level accuracy was obtained and regarded as the reference. The quantitative analysis where the position variations were evaluated and the qualitative analysis where the vehicle trajectories in three typical urban driving scenarios were discussed were both made for the three methods. The numerical results showed that the accuracy of the position variations from the SPP, KSPP, and TDCP methods was at the meter level, while that from the TDCP\/INS method improved to the centimeter level, and the accuracies were 1.9 cm, 2.9 cm, and 3.1 cm in the east, north, and upward directions. The trajectory results also demonstrated a perfect consistency of the driving positions between the TDCP\/INS method and the reference. As a contrast, the trajectories from the SPP and KFSPP methods had frequent jumps or sways when the vehicle drove along a large, curved road, turned at a crossroad, and passed under an urban viaduct.<\/jats:p>","DOI":"10.3390\/rs13234764","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T01:45:02Z","timestamp":1638323102000},"page":"4764","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stability Analysis of Position Datum for Real-Time GPS\/BDS\/INS Positioning in a Platform System with Multiple Moving Devices"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8199-8076","authenticated-orcid":false,"given":"Weiming","family":"Tang","sequence":"first","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangyang","family":"Li","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0248-9765","authenticated-orcid":false,"given":"Chenlong","family":"Deng","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuan","family":"Zou","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yawei","family":"Wang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kepei","family":"Qi","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/PL00012883","article-title":"Precise Point Positioning Using IGS Orbit and Clock Products","volume":"5","author":"Kouba","year":"2001","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sideris, M.G. (2009). Current state of precise point positioning and future prospects and limitations. Observing Our Changing Earth, Springer.","DOI":"10.1007\/978-3-540-85426-5"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s10291-015-0467-z","article-title":"Performance of real-time Precise Point Positioning using IGS real-time service","volume":"20","author":"Elsobeiey","year":"2016","journal-title":"GPS Solut."},{"key":"ref_4","unstructured":"Han, S., and Rizos, C. (1996, January 17\u201320). GPS Network Design and Error Mitigation For Real-Time Continuous Array Monitoring System. Proceedings of the 9th International Technical Meeting of the Satellite Division of US Inst Navigation, Kansas City, MO, USA."},{"key":"ref_5","unstructured":"Luo, N. (2000, January 19\u201322). Centimetre-Level Relative Positioning of Multiple Moving Platforms Using Ambiguity Constraints. Proceedings of the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2000), Salt Lake City, UT, USA."},{"key":"ref_6","unstructured":"Takasu, T., and Yasuda, A. (2009, January 4\u20136). Development of the Low-Cost RTK-GPS Receiver with an Open Source Program Package RTKLIB. Proceedings of the International Symposium on GPS\/GNSS, Jeju, Korea."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Li, T., Zhang, H., Niu, X., and Gao, Z. (2017). Tightly-Coupled Integration of Multi-GNSS Single-Frequency RTK and MEMS-IMU for Enhanced Positioning Performance. Sensors, 17.","DOI":"10.3390\/s17112462"},{"key":"ref_8","first-page":"48","article-title":"Kinematic GNSS positioning results compared against Agisoft Metashape and Pix4dmapper results produced in the San Joaquin experimental range in Fresno County, California","volume":"11","author":"Berber","year":"2021","journal-title":"J. G\u00e9od. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gurturk, M., and Soycan, M. (2021). Accuracy assessment of kinematic PPP versus PPK for GNSS flights data processing. Surv. Rev., 1\u20139.","DOI":"10.1080\/00396265.2020.1865016"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wu, Q., Sun, M., Zhou, C., and Zhang, P. (2019). Precise Point Positioning Using Dual-Frequency GNSS Observations on Smartphone. Sensors, 19.","DOI":"10.3390\/s19092189"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"360","DOI":"10.2174\/2213275912666190328201322","article-title":"Low Cost and Centimeter-Level Global Positioning System Accuracy Using Real-Time Kinematic Library and Real-Time Kinematic GPSA","volume":"14","author":"Gianey","year":"2021","journal-title":"Recent Adv. Comput. Sci. Commun."},{"key":"ref_12","unstructured":"Luo, N. (2001). Precise Relative Positioning of Multiple Moving Platforms Using Gps Carrier Phase Observables. [Ph.D. Thesis, University of Calgary]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s10291-020-0969-1","article-title":"Low-latency, high-rate, high-precision relative positioning with moving base in real time","volume":"24","author":"Dong","year":"2020","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5081\/jgps.7.1.1","article-title":"GPS RTK Performance Characteristics and Analysis","volume":"7","author":"Feng","year":"2008","journal-title":"J. Glob. Position. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s10291-013-0337-5","article-title":"Reliable single-epoch ambiguity resolution for short baselines using combined GPS\/BeiDou system","volume":"18","author":"Deng","year":"2014","journal-title":"GPS Solut."},{"key":"ref_16","first-page":"15","article-title":"A Kalman filter single point positioning for maritime applications using a smartphone","volume":"16","author":"Innac","year":"2020","journal-title":"Geogr. Tech."},{"key":"ref_17","unstructured":"RTCM Special Committee (2016). RTCM Standard 10403.3 Differential GNSS (Global Navigation Satellite Systems) Services-Version 3, RTCM."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/j.asr.2017.01.011","article-title":"The Multi-GNSS 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_19","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s00190-010-0439-6","article-title":"EVA: GPS-based extended velocity and acceleration determination","volume":"85","author":"Salazar","year":"2011","journal-title":"J. Geod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s10291-007-0083-7","article-title":"An approach to aid INS using time-differenced GPS carrier phase (TDCP) measurements","volume":"12","author":"Soon","year":"2008","journal-title":"GPS Solut."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1016\/j.ast.2004.07.003","article-title":"Tightly coupled GPS\/INS integration for missile applications","volume":"8","author":"Wendel","year":"2004","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10291-014-0425-1","article-title":"Time-differenced carrier phases technique for precise GNSS velocity estimation","volume":"19","author":"Freda","year":"2015","journal-title":"GPS Solut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1002\/j.2161-4296.2004.tb00359.x","article-title":"Precise Velocity Estimation Using a Stand-Alone GPS Receiver","volume":"51","author":"Soloviev","year":"2004","journal-title":"Navigation"},{"key":"ref_24","unstructured":"Groves, P.D. (2013). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House. [2nd ed.]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10291-015-0446-4","article-title":"Adaptive GPS\/INS integration for relative navigation","volume":"20","author":"Lee","year":"2015","journal-title":"GPS Solut."},{"key":"ref_26","unstructured":"Faulkner, N., Cooper, S., and Jeary, P. (2002, January 15\u201318). Integrated MEMS\/GPS Navigation Systems. Proceedings of the 2002 IEEE Position Location and Navigation Symposium (IEEE Cat. No.02CH37284), Palm Springs, CA, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1002\/j.2161-4296.2007.tb00403.x","article-title":"An Accurate Land-Vehicle MEMS IMU\/GPS Navigation System Using 3D Auxiliary Velocity Updates","volume":"54","author":"Niu","year":"2007","journal-title":"Navigation"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1186\/s43020-019-0001-5","article-title":"Inertial sensors technologies for navigation applications: State of the art and future trends","volume":"1","author":"Youssef","year":"2020","journal-title":"Satell. Navig."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Li, T., Zhang, H., Gao, Z., Chen, Q., and Niu, X. (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_30","doi-asserted-by":"crossref","first-page":"10599","DOI":"10.3390\/s130810599","article-title":"The Performance Analysis of a Real-Time Integrated INS\/GPS Vehicle Navigation System with Abnormal GPS Measurement Elimination","volume":"13","author":"Chiang","year":"2013","journal-title":"Sensors"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1109\/TAES.1987.310829","article-title":"Ionospheric Time-Delay Algorithm for Single-Frequency GPS Users","volume":"AES-23","author":"Klobuchar","year":"1987","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02521844","article-title":"Contributions to the theory of atmospheric refraction","volume":"105","author":"Saastamoinen","year":"1972","journal-title":"Bull. G\u00e9od."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kim, J., Park, M., Bae, Y., Kim, O.-J., Kim, D., Kim, B., and Kee, C. (2020). A Low-Cost, High-Precision Vehicle Navigation System for Deep Urban Multipath Environment Using TDCP Measurements. Sensors, 20.","DOI":"10.3390\/s20113254"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"25336","DOI":"10.3390\/s151025336","article-title":"GPS Cycle Slip Detection Considering Satellite Geometry Based on TDCP\/INS Integrated Navigation","volume":"15","author":"Kim","year":"2015","journal-title":"Sensors"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1029\/GL017i003p00199","article-title":"An Automatic Editing Algorithm for GPS data","volume":"17","author":"Blewitt","year":"1990","journal-title":"Geophys. Res. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1179\/1752270614Y.0000000099","article-title":"Development and evaluation of GNSS\/INS data processing software for position and orientation systems","volume":"47","author":"Niu","year":"2015","journal-title":"Surv. Rev."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/23\/4764\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:35:19Z","timestamp":1760168119000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/23\/4764"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,24]]},"references-count":36,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["rs13234764"],"URL":"https:\/\/doi.org\/10.3390\/rs13234764","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,24]]}}}