{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:01:03Z","timestamp":1760238063164,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2020,7,2]],"date-time":"2020-07-02T00:00:00Z","timestamp":1593648000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In high-precision GPS precise point positioning (PPP) time transfer, errors caused by the effect of ionosphere delay have to be corrected. Usually the ionosphere-free combinations of the pseudo code and the carrier phase is used in GPS PPP data processing, and it effectively eliminates the effect of the first-order ionospheric delay. This study quantitatively analyzes the errors caused by higher-order ionospheric (Ion2+) delays in precise PPP time transfer. Data of two 7-day test periods, including low and moderate ionospheric conditions, from 20 stations located in middle- and low-latitude, were analyzed. The difference in clock solution with and without the Ion2+ correction, including the receiver clock solution and time-link clock solution, was deeply analyzed and discussed. The difference sequence shows a constant bias plus some variations with a diurnal variation. For the difference of the receiver clock solutions, the mean standard deviation of the variations is 3.92 ps in low-latitude, which is much larger than that of 2.59 ps in mid-latitude due to the influence of the larger ionospheric electron density on the low-latitude. The maximum constant bias reached more than 15 ps and was negative at most stations in the northern hemisphere, while it was positive at most stations located in the southern hemisphere. The difference in the time-link solutions correlates not only with time and region, but also with the length of the time-links. The largest difference in the long time-link SYDN-PTBB, BJNM-SYDN, AMC2-SYDN, etc., reaches more than 25 ps, while that of the short time-link IENG-PTBB, BRUX-PTBB, etc., is less than 3.5 ps. Therefore, the Ion2+ correction is necessary for high-precision PPP time transfer over long time-links, especially time-links made by one station located in the northern hemisphere and another located in the south hemisphere; however, it could be ignored for short time-links.<\/jats:p>","DOI":"10.3390\/rs12132129","type":"journal-article","created":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T06:51:20Z","timestamp":1593759080000},"page":"2129","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Evaluation of the Effect of Higher-Order Ionospheric Delay on GPS Precise Point Positioning Time Transfer"],"prefix":"10.3390","volume":"12","author":[{"given":"Haiyan","family":"Yang","sequence":"first","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precision Navigation and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuhai","family":"Yang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precision Navigation and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precision Navigation and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoqi","family":"Sun","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precision Navigation and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":"Key Laboratory of Precision Navigation and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Petit, G., Harmegnies, A., Mercier, F., Perosanz, F., and Loyer, S. (2011, January 2\u20135). The time stability of PPP links for TAI. Proceedings of the Joint Meeting European Frequency and Time Forum and IEEE International Frequency Control Symposium, San Francisco, CA, USA.","DOI":"10.1109\/FCS.2011.5977299"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1088\/0026-1394\/52\/2\/301","article-title":"1 \u00d7 10\u221216 frequency transfer by GPS PPP with integer ambiguity resolution","volume":"52","author":"Petit","year":"2015","journal-title":"Metrologia"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Defraigne, P., Guyennon, N., and Bruyn, C. (2008). GPS time and frequency transfer: PPP and phase-only analysis. Int. J. Navig. Obs., 175468.","DOI":"10.1155\/2008\/175468"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s10291-014-0377-5","article-title":"Monitoring of UTC(k)\u2019s using PPP and IGS real-time products","volume":"19","author":"Defraigne","year":"2015","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, P., Tu, R., Zhang, R., Gao, Y., and Cai, H. (2018). Combining GPS, BeiDou, and Galileo Satellite Systems for Time and Frequency Transfer Based on Carrier Phase Observations. Remote Sens., 10.","DOI":"10.3390\/rs10020324"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ge, Y., Dai, P., Qin, W., Yang, X., Zhou, F., Wang, S., and Zhao, X. (2019). Performance of Multi-GNSS Precise Point Positioning Time and Frequency Transfer with Clock Modeling. Remote Sens., 11.","DOI":"10.3390\/rs11030347"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Su, K., Jin, S., and Hoque, M. (2019). Evaluation of Ionospheric Delay Effects on Multi-GNSS Positioning Performance. Remote Sens., 11.","DOI":"10.3390\/rs11020171"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1002\/2013RS005212","article-title":"Ionospheric corrections for GPS time transfer","volume":"49","author":"Rose","year":"2014","journal-title":"Radio Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhang, J., Gao, J., Yu, B., Sheng, C., and Gan, X. (2020). Research on Remote GPS Common-View Precise Time Transfer Based on Different Ionosphere Disturbances. Sensors, 20.","DOI":"10.3390\/s20082290"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s10291-011-0220-1","article-title":"RINEX_HO: Second-and third-order ionospheric corrections for RINEX observation files","volume":"15","author":"Marques","year":"2011","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s10712-010-9105-z","article-title":"A review of higher order ionospheric refraction effects on dual frequency GPS","volume":"32","author":"Petrie","year":"2011","journal-title":"Surv. Geophys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3823","DOI":"10.1002\/2013JB010568","article-title":"Distribution and mitigation of higher-order ionospheric effects on precise GNSS processing","volume":"119","author":"Defraigne","year":"2014","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_13","first-page":"883","article-title":"Influence of higher-order ionospheric delay correction on static precise point positioning","volume":"38","author":"Zhang","year":"2013","journal-title":"Inf. Sci. Wuhan Univ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1088\/1361-6501\/aaf555","article-title":"Effect analysis of higher-order ionospheric corrections on quad-constellation GNSS PPP","volume":"30","author":"Cai","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"9420","DOI":"10.1002\/2017JB014750","article-title":"Impact and implementation of higher-order ionospheric effects on precise GNSS applications","volume":"122","author":"Hadas","year":"2017","journal-title":"J. Geophys. Res. B Solid Earth"},{"key":"ref_16","first-page":"B08417","article-title":"Correction to \u201csecond-order ionospheric term in GPS: Implementation and impact on geodetic estimates\u201d","volume":"112","author":"Juan","year":"2007","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.geog.2016.06.005","article-title":"Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning","volume":"7","author":"Liu","year":"2016","journal-title":"Geod. Geodyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s00190-006-0106-0","article-title":"Higher order ionospheric effects in precise GNSS positioning","volume":"81","author":"Hoque","year":"2007","journal-title":"J. Geod."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1017\/S0373463311000531","article-title":"On Modelling of Second-Order Ionospheric Delay for GPS Precise Point Positioning","volume":"65","author":"Elsobeiey","year":"2012","journal-title":"J. Navig."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1016\/j.asr.2013.12.037","article-title":"Effects on noise properties of GPS time series caused by higher-order ionospheric corrections","volume":"53","author":"Jiang","year":"2014","journal-title":"Adv. Space Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1817","DOI":"10.1007\/s10291-017-0655-0","article-title":"On the estimation of higher-order ionospheric effects in precise point positioning","volume":"21","author":"Banville","year":"2017","journal-title":"GPS Solut."},{"key":"ref_22","first-page":"45","article-title":"Impact of Second Order Ionosphere Delays for GPS Kinematic Precise Point Positioning Applications","volume":"47","author":"Zhang","year":"2018","journal-title":"Acta Geodaetica et Cartographica Sinica."},{"key":"ref_23","unstructured":"Boehm, J., Hernandez-Pajares, M., Hugentobler, U., Hulley, G., Mercier, F., Niell, A., and Pavlis, E. (2010). Chapter 9: Models for Atmospheric Propagation Delays. IERS Technical Note No. 36, IERS. IERS Conventions."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Teunissen, P.J., and Montenbruck, O. (2017). The international GNSS Service. Springer Handbook of Global Navigation Satellite Systems, Springer International Publishing.","DOI":"10.1007\/978-3-319-42928-1"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1016\/j.asr.2009.07.011","article-title":"Influence of ionospheric perturbations in GPS time and frequency transfer","volume":"45","author":"Pireaux","year":"2009","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s10291-009-0152-1","article-title":"Higher-order ionospheric effects in GPS time and frequency transfer","volume":"14","author":"Pireaux","year":"2010","journal-title":"GPS Solut."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Hoque, M., Jakowski, N., and Berdermann, J. (2017). Transionospheric Microwave Propagation: Higher-Order Effects up to 100 GHz, Intech Open Science Open Minds.","DOI":"10.5772\/66659"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1186\/s40623-015-0228-9","article-title":"International Geomagnetic Reference Field: The 12th generation","volume":"67","author":"Finlay","year":"2015","journal-title":"Earth Planet Space"},{"key":"ref_29","unstructured":"Dach, R., Lutz, S., Walser, P., and Fridez, P. (2015). Bernese GNSS Software Version 5.2, User Manual; Astronomical Institute, Universtiy of Bern."},{"key":"ref_30","unstructured":"Gurtner, W., and Estey, L. (2007). RINEX: The Receiver Independent Exchange Format Version 2.11, Astronomical Institute, University of Bern."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Yang, H., Yang, X., Zhang, Z., and Zhao, K. (2018). High-Precision Ionosphere Monitoring Using Continuous Measurements from BDS GEO Satellites. Sensors, 18.","DOI":"10.3390\/s18030714"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/TUFFC.2003.1209545","article-title":"Developing an IGS time scale","volume":"50","author":"Senior","year":"2003","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1016\/j.asr.2018.10.031","article-title":"Analysis of the data processing strategies of spherical harmonic expansion model on global ionosphere mapping for moderate solar activity","volume":"63","author":"Zhang","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_34","unstructured":"Schaer, S., Gurtner, W., and Feltens, J. (1998, January 9\u201311). IONEX: The IONosphere Map EXchange format version 1. Proceedings of the IGS Analysis Center Workshop, Darmstadt, Germany."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/13\/2129\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:46:38Z","timestamp":1760175998000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/13\/2129"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,2]]},"references-count":34,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["rs12132129"],"URL":"https:\/\/doi.org\/10.3390\/rs12132129","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2020,7,2]]}}}