{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:24:40Z","timestamp":1760149480763,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T00:00:00Z","timestamp":1691366400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Young Elite Scientists Sponsorship Program by CAST","award":["2022QNRC001","62201028"],"award-info":[{"award-number":["2022QNRC001","62201028"]}]},{"name":"National Natural Science Foundation for Young Scientists of China","award":["2022QNRC001","62201028"],"award-info":[{"award-number":["2022QNRC001","62201028"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Performing the high-precision Global Navigation Satellite System (GNSS) applications with low-cost antennas is an up-and-coming research field. However, the antenna-induced phase biases, i.e., phase center corrections (PCCs), of the low-cost antennas can be up to centimeters and need to be calibrated in advance. The relative field antenna calibration method is easy to conduct, but the classical procedure entails integer ambiguity resolution, which may face the problem of low success rate under the centimeter-level PCCs. In this contribution, we designed a relative field calibration method suitable for the low-cost GNSS antennas. The triple-differencing operations were utilized to eliminate the carrier-phase ambiguities and then construct PCC measurements; the time-differencing interval was set to a relatively long time span, such as one hour, and the reference satellite was selected according to the angular distance it passed over during a time-differencing interval. To reduce the effect of significant triple-differencing noise, a weight setting method based on the area of a spherical quadrilateral was proposed for the spherical harmonics fitting process. The duration of the data collection with respect to GPS and BDS was discussed. The performance of the proposed method was assessed with real GPS and BDS observations and a variety of simulated phase patterns, showing that calibration results could be obtained with millimeter-level accuracy. The impact of cycle slip and elevation mask angle on the calibration results was also analyzed.<\/jats:p>","DOI":"10.3390\/rs15153917","type":"journal-article","created":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T12:38:59Z","timestamp":1691498339000},"page":"3917","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Relative Field Antenna Calibration Method Designed for Low-Cost GNSS Antennas by Exploiting Triple-Differenced Measurements"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9411-1136","authenticated-orcid":false,"given":"Wenxin","family":"Jin","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenfei","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianwei","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"},{"name":"College of Fashion Art and Engineering, Beijing Institute of Fashion Technology, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1002\/j.2161-4296.1994.tb01881.x","article-title":"Signal Characteristics of GPS User Antennas","volume":"41","author":"Schupler","year":"1994","journal-title":"Navigation"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s10291-022-01339-8","article-title":"Offsets in the EPN station position time series resulting from antenna\/radome changes: PCC type-dependent model analyses","volume":"27","author":"Dawidowicz","year":"2022","journal-title":"GPS Solut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1179\/1752270613Y.0000000043","article-title":"Impact of different GNSS antenna calibration models on height determination in the ASG-EUPOS network: A case study","volume":"45","author":"Dawidowicz","year":"2013","journal-title":"Surv. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1002\/j.2161-4296.1997.tb02346.x","article-title":"A New Approach for Field Calibration of Absolute GPS Antenna Phase Center Variations","volume":"44","author":"Schmitz","year":"1997","journal-title":"Navigation"},{"key":"ref_5","unstructured":"W\u00fcbbena, G., Schmitz, M., Menge, F., B\u00f6der, V., and Seeber, G. (2000, January 19\u201322). Automated Absolute Field Calibration of GPS Antennas in Real-Time. 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":"Bilich, A., and Mader, G.L. (2010, January 21\u201324). GNSS absolute antenna calibration at the national geodetic survey. Proceedings of the 23rd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1007\/s10291-005-0015-3","article-title":"Absolute calibration of GPS antennas: Laboratory results and comparison with field and robot techniques","volume":"10","author":"Campbell","year":"2006","journal-title":"GPS Solut."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4932","DOI":"10.1016\/j.asr.2021.01.029","article-title":"Multi-frequency multi-GNSS receiver antenna calibration at IfE: Concept-calibration results-validation","volume":"68","author":"Kersten","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1007\/s10291-020-00999-8","article-title":"Absolute robotic GNSS antenna calibrations in open field environment","volume":"24","author":"Sutyagin","year":"2020","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"28717","DOI":"10.3390\/s151128717","article-title":"First Results of Field Absolute Calibration of the GPS Receiver Antenna at Wuhan University","volume":"15","author":"Hu","year":"2015","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Willi, D., Koch, D., Meindl, M., and Rothacher, M. (2018, January 24\u201328). Absolute GNSS Antenna Phase Center Calibration with a Robot. Proceedings of the 31st International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2018), Miami, FL, USA.","DOI":"10.33012\/2018.16040"},{"key":"ref_12","unstructured":"Rothacher, M., Schaer, S., Mervart, L., and Beutler, G. (1995). IGS Workshop Proceedings: Special Topics and New Directions, GeoForschungsZentrum."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/PL00012780","article-title":"GPS Antenna Calibration at the National Geodetic Survey","volume":"3","author":"Mader","year":"1999","journal-title":"GPS Solut."},{"key":"ref_14","first-page":"49","article-title":"Calibrating antenna phase centers","volume":"16","author":"Akrour","year":"2005","journal-title":"GPS World"},{"key":"ref_15","unstructured":"Biagi, L., Grec, F.-C., Fermi, A., and Negretti, M. (2023, January 25). Relative Antenna Calibration for Mass-Market GNSS Receivers: A Case Study. Available online: https:\/\/www.researchgate.net\/profile\/Florin-Catalin-Grec\/publication\/328074695_Relative_antenna_calibration_for_mass-market_GNSS_receivers_A_case_study\/links\/5bb626184585153610ac0b53\/Relative-antenna-calibration-for-mass-market-GNSS-receivers-A-case-study.pdf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1002\/navi.273","article-title":"GNSS antenna phase center variation calibration for attitude determination on short baselines","volume":"65","author":"Willi","year":"2018","journal-title":"Navigation"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Krietemeyer, A., Van Der Marel, H., Van De Giesen, N., and Ten Veldhuis, M.-C. (2022). A Field Calibration Solution to Achieve High-Grade-Level Performance for Low-Cost Dual-Frequency GNSS Receiver and Antennas. Sensors, 22.","DOI":"10.3390\/s22062267"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhou, R., Hu, Z., Zhao, Q., Cai, H., Liu, X., Liu, C., Wang, G., Kan, H., and Chen, L. (2022). Consistency Analysis of the GNSS Antenna Phase Center Correction Models. Remote Sens., 14.","DOI":"10.3390\/rs14030540"},{"key":"ref_19","unstructured":"Rao, B.R., Kunysz, W., Fante, R., and McDonald, K. (2013). GPS\/GNSS Antennas, Artech House."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/s10291-019-0941-0","article-title":"Absolute field calibration for multi-GNSS receiver antennas at ETH Zurich","volume":"24","author":"Willi","year":"2019","journal-title":"GPS Solut."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Leick, A., Rapoport, L., and Tatarnikov, D. (2015). GPS Satellite Surveying, John Wiley & Sons. [4th ed.].","DOI":"10.1002\/9781119018612"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s00190-010-0426-y","article-title":"A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver","volume":"85","author":"Liu","year":"2011","journal-title":"J. Geodesy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10291-012-0275-7","article-title":"Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity","volume":"17","author":"Cai","year":"2013","journal-title":"GPS Solut."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s10291-015-0456-2","article-title":"Benefits of the third frequency signal on cycle slip correction","volume":"20","author":"Zhang","year":"2016","journal-title":"GPS Solut."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s10291-011-0249-1","article-title":"MATLAB software for GPS cycle-slip processing","volume":"16","author":"Dai","year":"2012","journal-title":"GPS Solut."},{"key":"ref_26","unstructured":"Karaim, M.O., Karamat, T.B., Noureldin, A., Tamazin, M., and Atia, M.M. (2013, January 16\u201320). Real-time Cycle-slip Detection and Correction for Land Vehicle Navigation using Inertial Aiding. Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, USA."},{"key":"ref_27","unstructured":"(2023, June 25). IGS RINEX WG RTCM-SC104. RINEX The Receiver Independent Exchange Format, Version 3.04. Available online: https:\/\/files.igs.org\/pub\/data\/format\/rinex304.pdf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1002\/j.2161-4296.2002.tb00269.x","article-title":"Instantaneous Real-Time Cycle-Slip Correction for Quality Control of GPS Carrier-Phase Measurements","volume":"49","author":"Kim","year":"2002","journal-title":"Navigation"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"075108","DOI":"10.1088\/0957-0233\/20\/7\/075108","article-title":"An integer ambiguity resolution method for the global positioning system (GPS)-based land vehicle attitude determination","volume":"20","author":"Wang","year":"2009","journal-title":"Meas. Sci. Technol."},{"key":"ref_30","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_31","unstructured":"Hilla, S. (2023, April 05). The Extended Standard Product 3 Orbit Format (SP3-d). Available online: https:\/\/files.igs.org\/pub\/data\/format\/sp3d.pdf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1017\/S0373463307004250","article-title":"Assessment of several interpolation methods for precise GPS orbit","volume":"60","author":"Yousif","year":"2007","journal-title":"J. Navig."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s10291-021-01130-1","article-title":"An effective interpolation strategy for mitigating the day boundary discontinuities of precise GNSS orbit products","volume":"25","author":"Song","year":"2021","journal-title":"GPS Solut."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Dawidowicz, K., Rapi\u0144ski, J., \u015amieja, M., Wielgosz, P., Kwa\u015bniak, D., Jarmo\u0142owski, W., Grzegory, T., Tomaszewski, D., Janicka, J., and Go\u0142aszewski, P. (2021). Preliminary Results of an Astri\/UWM EGNSS Receiver Antenna Calibration Facility. Sensors, 21.","DOI":"10.3390\/s21144639"},{"key":"ref_35","unstructured":"Rothacher, M., and Schmid, R. (2023, May 05). ANTEX: The Antenna Exchange Format, Version 1.4. Available online: https:\/\/files.igs.org\/pub\/station\/general\/antex14.txt."},{"key":"ref_36","unstructured":"Van Diggelen, F. (2009). A-GPS: Assisted GPS, GNSS, and SBAS, Artech House."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2735","DOI":"10.1016\/j.asr.2018.01.019","article-title":"Analysis of the carrier-phase multipath in GNSS triple-frequency observation combinations","volume":"63","author":"Gao","year":"2019","journal-title":"Adv. Space Res."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/15\/3917\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:27:36Z","timestamp":1760128056000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/15\/3917"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,7]]},"references-count":37,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["rs15153917"],"URL":"https:\/\/doi.org\/10.3390\/rs15153917","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,8,7]]}}}