{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:47:23Z","timestamp":1761677243861,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:00:00Z","timestamp":1699833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2021MD703896","YNKJXM20220033","42074045","42374043"],"award-info":[{"award-number":["2021MD703896","YNKJXM20220033","42074045","42374043"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and technology project of China Southern Power Grid Yunnan Power Grid Co., Ltd.","award":["2021MD703896","YNKJXM20220033","42074045","42374043"],"award-info":[{"award-number":["2021MD703896","YNKJXM20220033","42074045","42374043"]}]},{"name":"China Natural Science Funds","award":["2021MD703896","YNKJXM20220033","42074045","42374043"],"award-info":[{"award-number":["2021MD703896","YNKJXM20220033","42074045","42374043"]}]},{"name":"Independent Project of the State Key Laboratory of China","award":["2021MD703896","YNKJXM20220033","42074045","42374043"],"award-info":[{"award-number":["2021MD703896","YNKJXM20220033","42074045","42374043"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Given the potential of low-earth orbit (LEO) satellites in terms of navigation enhancement, accurately estimating the differential code bias (DCB) of GNSS satellites and LEO satellites is an important research topic. In this study, to obtain accurate DCB estimates, the effects of vertical total electron content (VTEC) modeling parameters of the topside ionosphere on DCB estimation were investigated using LEO observations for the first time. Different modeling parameters were set in the DCB estimations, encompassing modeling spacing in the dynamic temporal mode and degree and order (D&amp;O) in spherical harmonic modeling. The DCB precisions were then evaluated, and the impacts were analyzed. Thus, a number of crucial and beneficial conclusions are drawn: (1) The maximum differences in the GPS DCB estimates after adopting different modeling spacings and different D&amp;Os exhibit that the different modeling spacings or D&amp;Os both affect the GPS DCB estimates and their root-mean square (RMS), and the effects of the two are at the same level. (2) The maximum differences in receiver DCBs using different modeling spacings indicate that the modeling spacing has a significant impact on the receiver DCBs, compared with GPS DCBs. Whereas, the maximum differences in receiver DCBs with different modeling D&amp;Os are inferior to the differences in the GPS DCBs. That is, the modeling spacing has a greater impact on the LEO DCBs than those of the modeling D&amp;O. (3) The experimental results indicate that the GPS DCB estimates using a modeling spacing of 12H have higher precisions than the others, whereas LEO receiver DCBs using a spacing of 4H or 6H obtain optimal STD. In terms of modeling D&amp;O, adopting 8D&amp;O in the LEO-based VTEC modeling can attain superior estimates and precisions for both GPS and LEO DCBs. The research conclusions can provide references for LEO-augmented DCB estimation.<\/jats:p>","DOI":"10.3390\/rs15225335","type":"journal-article","created":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T02:46:47Z","timestamp":1699843607000},"page":"5335","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Effects of Topside Ionosphere Modeling Parameters on Differential Code Bias (DCB) Estimation Using LEO Satellite Observations"],"prefix":"10.3390","volume":"15","author":[{"given":"Yifan","family":"Wang","sequence":"first","affiliation":[{"name":"Joint Laboratory of Power Remote Sensing Technology, Electric Power Research Institute, Yunnan Power Grid Co., Ltd., Kunming 650217, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1520-5442","authenticated-orcid":false,"given":"Mingming","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}]},{"given":"Yunbin","family":"Yuan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}]},{"given":"Guofang","family":"Wang","sequence":"additional","affiliation":[{"name":"Joint Laboratory of Power Remote Sensing Technology, Electric Power Research Institute, Yunnan Power Grid Co., Ltd., Kunming 650217, China"}]},{"given":"Hao","family":"Geng","sequence":"additional","affiliation":[{"name":"Joint Laboratory of Power Remote Sensing Technology, Electric Power Research Institute, Yunnan Power Grid Co., Ltd., Kunming 650217, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,13]]},"reference":[{"key":"ref_1","unstructured":"Schaer, S. (1999). Mapping and Predicting the Earth\u2019s Ionosphere Using the Global Positioning System. [Ph.D. Dissertation, University of Berne]."},{"key":"ref_2","unstructured":"Yuan, Y. (2002). Study on Theories and Methods of Correcting Ionospheric Delay and Monitoring Ionosphere Based on GPS. [Ph.D. Dissertation, Institute of Geodesy and Geophysics, Chinese Academy of Sciences]."},{"key":"ref_3","unstructured":"Dach, R., Schaer, S., Hugentobler, U., Schildknecht, T., and G\u00e4de, A. (2006, January 27\u201330). Combined multi-system GNSS analysis for time and frequency transfer. Proceedings of the 20th European Frequency and Time Forum, Braunschweig, Germany."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1007\/s00190-011-0508-5","article-title":"The ionosphere: Effects, GPS modeling and the benefits for space geodetic techniques","volume":"85","author":"Juan","year":"2011","journal-title":"J. Geod."},{"key":"ref_5","unstructured":"Montenbruck, O., and Hauschild, A. (2013, January 27\u201329). Code biases in multi-GNSS point positioning. Proceedings of the 2013 International Technical Meeting of the Institute of Navigation, San Diego, CA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1002\/navi.64","article-title":"Diferential code bias estimation using Multi-GNSS observations and global ionosphere maps","volume":"61","author":"Montenbruck","year":"2014","journal-title":"Navigation"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s00190-015-0867-4","article-title":"Determination of differential code biases with multi-GNSS observations","volume":"90","author":"Wang","year":"2016","journal-title":"J. Geod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s00190-021-01549-x","article-title":"Estimation of code observation-specific biases (OSBs) for the modernized multi-frequency and multi-GNSS signals: An undifferenced and uncombined approach","volume":"95","author":"Liu","year":"2021","journal-title":"J. Geod."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1029\/97RS02707","article-title":"A global mapping technique for GPS-derived ionospheric total electron content measurements","volume":"33","author":"Mannucci","year":"1998","journal-title":"Radio Sci."},{"key":"ref_10","unstructured":"Schaer, S., Gurtner, W., and Feltens, J. (1998, January 9\u201311). IONEX: The ionosphere map exchange format version 1. Proceedings of the IGS AC Workshop, Darmstadt, Germany."},{"key":"ref_11","unstructured":"Schaer, S. (2008, January 2\u20136). Differential code biases (DCB) in GNSS analysis. Proceedings of the IGS Workshop, Miami Beach, FL, USA."},{"key":"ref_12","unstructured":"Meindl, M., Dach, R., and Jean, Y. (2012). IGS Technical Report 2011, Astronomical Institute, University of Berne."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1016\/j.asr.2008.05.014","article-title":"The occurrence of themid-latitude ionospheric trough in GPS-TEC measurements","volume":"43","author":"Krankowski","year":"2009","journal-title":"Adv. Space Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1080\/10020070412331344711","article-title":"A generalized trigonometric series function model for determining ionospheric delay","volume":"14","author":"Yuan","year":"2004","journal-title":"Prog. Nat. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1007\/s00190-012-0565-4","article-title":"Two-step method for the determination of the differential code biases of COMPASS satellites","volume":"86","author":"Li","year":"2012","journal-title":"J. Geod."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s10291-014-0433-1","article-title":"Estimation and analysis of GPS satellite DCB based on LEO observations","volume":"20","author":"Lin","year":"2014","journal-title":"GPS Solut."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s10291-015-0437-5","article-title":"Is the long-term variation of the estimated GPS differential code biases associated with ionospheric variability?","volume":"20","author":"Zhong","year":"2015","journal-title":"GPS Solut."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s10291-012-0279-3","article-title":"M_DCB: Matlab code for estimating GNSS satellite and receiver differential code biases","volume":"16","author":"Jin","year":"2012","journal-title":"GPS Solut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1007\/s10291-017-0638-1","article-title":"Computation of GPS P1\u2013P2 Differential Code Biases with JASON-2","volume":"21","author":"Wautelet","year":"2017","journal-title":"GPS Solut."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1002\/2016JA023375","article-title":"Modeling the plasmasphere based on LEO satellites onboard GPS measurements","volume":"122","author":"Chen","year":"2017","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, W., Li, M., Shi, C., Fang, R., Zhao, Q., Meng, X., and Bai, W. (2017). GPS and BeiDou Differential Code Bias Estimation Using Fengyun-3C Satellite Onboard GNSS Observations. Remote Sens., 9.","DOI":"10.3390\/rs9121239"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10291-019-0850-2","article-title":"FY-3D and FY-3C onboard observations for differential code biases estimation","volume":"23","author":"Li","year":"2019","journal-title":"GPS Solut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.asr.2019.10.005","article-title":"Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations","volume":"65","author":"Zhou","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s00190-020-01415-2","article-title":"Mapping topside ionospheric vertical electron content from multiple LEO satellites at different orbital altitudes","volume":"94","author":"Ren","year":"2020","journal-title":"J. Geod."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s00190-020-01458-5","article-title":"Simultaneous estimation of GPS P1\u2013P2 differential code biases using low earth orbit satellites data from two different orbit heights","volume":"94","author":"Liu","year":"2020","journal-title":"J. Geod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1002\/2015SW001162","article-title":"How can GOCE and TerraSAR-X contribute to the topside ionosphere and plasmasphere research?","volume":"13","author":"Zakharenkova","year":"2015","journal-title":"Space Weather"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4896","DOI":"10.1109\/TGRS.2016.2552542","article-title":"Determination of differential code bias of GNSS receiver onboard low earth orbit satellite","volume":"54","author":"Zhong","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","first-page":"377","article-title":"Estimation of COSMIC LEO satellite GPS receiver differential code bias","volume":"57","author":"Zhang","year":"2014","journal-title":"Chin. J. Geophys."},{"key":"ref_29","unstructured":"Wen, H., Kruizingga, G., Paik, M., Landerer, F., Bertiger, W., Sakumura, C., Bandikova, T., and Mccullough, C. (2019). Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) Level-1 Data Product User Handbook, NASA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111-1","DOI":"10.1029\/2001GL013744","article-title":"A simple \u201cgeometric\u201d mapping function for the hydrostatic delay at radio frequencies and assessment of its performance","volume":"29","author":"Foelsche","year":"2002","journal-title":"Geophys. Res. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"S09001","DOI":"10.1029\/2011SW000687","article-title":"Quantitative evaluation of the low Earth orbit satellite based slant total electron content determination","volume":"9","author":"Yue","year":"2011","journal-title":"Space Weather"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s10291-015-0444-6","article-title":"Assessment of vertical TEC mapping functions for space-based GNSS observations","volume":"20","author":"Zhong","year":"2015","journal-title":"GPS Solut."},{"key":"ref_33","unstructured":"Klobuchar, J.A. (1975). A First-Order World-Wide Ionospheric Time-Delay Algorithm, Air Force Cambridge Research Labs.. No. 324."},{"key":"ref_34","unstructured":"IGS (2012). IGS Technical Report 2011, Astronomical Institute, University of Berne."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1007\/s10291-017-0634-5","article-title":"GPS differential code biases determination: Methodology and analysis","volume":"21","author":"Sanz","year":"2017","journal-title":"GPS Solut."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s00190-006-0029-9","article-title":"Pseudo-Stochastic orbit modeling techniques for Low-Earth Orbiters","volume":"80","author":"Hugentobler","year":"2006","journal-title":"J. Geod."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1007\/s00190-006-0073-5","article-title":"Precise orbit determination for the GRACE mission using only GPS data","volume":"80","author":"Kang","year":"2006","journal-title":"J. Geod."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s10291-008-0091-2","article-title":"Tracking and orbit determination performance of the GRAS instrument on MetOp-A","volume":"12","author":"Montenbruck","year":"2008","journal-title":"GPS Solut."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00190-008-0256-3","article-title":"Precise orbit determination for the FORMOSAT-3\/COSMIC satellite mission using GPS","volume":"83","author":"Hwang","year":"2008","journal-title":"J. Geod."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1080\/01490419.2010.488966","article-title":"Precision Orbit Determination Standards for the Jason Series of Altimeter Missions","volume":"33","author":"Cerri","year":"2010","journal-title":"Mar. Geod."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Liu, M., Yuan, Y., Ou, J., and Chai, Y. (2019). Research on Attitude Models and Antenna Phase Center Correction for Jason-3 Satellite Orbit Determination. Sensors, 19.","DOI":"10.3390\/s19102408"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/22\/5335\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:22:01Z","timestamp":1760131321000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/22\/5335"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,13]]},"references-count":41,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["rs15225335"],"URL":"https:\/\/doi.org\/10.3390\/rs15225335","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,11,13]]}}}