{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:11:49Z","timestamp":1760242309175,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,20]],"date-time":"2017-03-20T00:00:00Z","timestamp":1489968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41474018","41274032","41210006"],"award-info":[{"award-number":["41474018","41274032","41210006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Beijing Key Laboratory of Urban Spatial Information Engineering","award":["2016204"],"award-info":[{"award-number":["2016204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Swarm is a European Space Agency (ESA) project that was launched on 22 November 2013, which consists of three Swarm satellites. Swarm precise orbits are essential to the success of the above project. This study investigates how well Swarm zero-differenced (ZD) reduced-dynamic orbit solutions can be determined using space-borne GPS data and optimized pseudo-stochastic pulses under high ionospheric activity. We choose Swarm space-borne GPS data from 1\u201325 October 2014, and Swarm reduced-dynamic orbits are obtained. Orbit quality is assessed by GPS phase observation residuals and compared with Precise Science Orbits (PSOs) released by ESA. Results show that pseudo-stochastic pulses with a time interval of 6 min and a priori standard deviation (STD) of 10\u22122 mm\/s in radial (R), along-track (T) and cross-track (N) directions are optimized to Swarm ZD reduced-dynamic precise orbit determination (POD). During high ionospheric activity, the mean Root Mean Square (RMS) of Swarm GPS phase residuals is at 9\u201311 mm, Swarm orbit solutions are also compared with Swarm PSOs released by ESA and the accuracy of Swarm orbits can reach 2\u20134 cm in R, T and N directions. Independent Satellite Laser Ranging (SLR) validation indicates that Swarm reduced-dynamic orbits have an accuracy of 2\u20134 cm. Swarm-B orbit quality is better than those of Swarm-A and Swarm-C. The Swarm orbits can be applied to the geomagnetic, geoelectric and gravity field recovery.<\/jats:p>","DOI":"10.3390\/s17030635","type":"journal-article","created":{"date-parts":[[2017,3,20]],"date-time":"2017-03-20T11:39:09Z","timestamp":1490009949000},"page":"635","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Precise Orbit Solution for Swarm Using Space-Borne GPS Data and Optimized Pseudo-Stochastic Pulses"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0084-3206","authenticated-orcid":false,"given":"Bingbing","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"given":"Zhengtao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"given":"Lv","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Beijing Key Laboratory of Urban Spatial Information Engineering, Beijing Institute of Surveying and Mapping, Beijing 100038, China"}]},{"given":"Jiandi","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"given":"Yaodong","family":"Qiu","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"given":"Fupeng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.asr.2006.10.008","article-title":"Swarm\u2014An earth observation mission investigating geospace","volume":"41","author":"Knudsen","year":"2008","journal-title":"Adv. Space Res."},{"key":"ref_2","first-page":"218","article-title":"Swarm kinematic orbits and gravity fields from 18 months of GPS data","volume":"57","author":"Dahle","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1016\/j.asr.2015.06.002","article-title":"Precise science orbits for the Swarm satellite constellation","volume":"56","author":"Doornbos","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_4","unstructured":"Kuang, D., Bar-Sever, Y., Bertiger, W., Desai, S., Haines, B., Iijima, B., Kruizinga, G., Meehan, T., and Romans, L. (2001, January 22\u201324). Precision Orbit Determination for CHAMP Using GPS Data from Black Jack Receiver. Proceedings of the 2001 National Technical Meeting of the Institute of Navigation, Long Beach, CA, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1875","DOI":"10.1016\/S0273-1177(03)00159-5","article-title":"Precise orbit determination for GRACE","volume":"31","author":"Kang","year":"2003","journal-title":"Adv. Space Res."},{"key":"ref_6","unstructured":"Boomkamp, H., and Koenig, R. (2005). 2004 Berne Workshop and Symposium, Astronomical Institute, University of Berne."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s00190-004-0379-0","article-title":"Integrated adjustment of CHAMP, GRACE and GPS data","volume":"78","author":"Zhu","year":"2004","journal-title":"J. Geod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0273-1177(95)98781-I","article-title":"Precise orbit determination for TOPEX\/Poseidon using GPS-SST data","volume":"16","author":"Kang","year":"1995","journal-title":"Adv. Space Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1016\/S0273-1177(03)00161-3","article-title":"Champ precise orbit determination using GPS data","volume":"31","author":"Visser","year":"2003","journal-title":"Adv. Space Res."},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"1612","DOI":"10.1016\/j.asr.2007.03.012","article-title":"Precise orbit determination for GRACE using undifferenced or doubly differenced GPS data","volume":"39","author":"Hugentobler","year":"2007","journal-title":"Adv. Space Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"47","DOI":"10.5194\/adgeo-1-47-2003","article-title":"Kinematic and reduced-dynamic precise orbit determination of low Earth orbiters","volume":"1","author":"Svehla","year":"2003","journal-title":"Adv. Geosci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S0273-1177(02)00298-3","article-title":"Efficient precise orbit determination of LEO satellites using GPS","volume":"30","author":"Bock","year":"2002","journal-title":"Adv. Space Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1007\/s00190-014-0742-8","article-title":"GOCE: Precise orbit determination for the entire mission","volume":"88","author":"Bock","year":"2014","journal-title":"J. Geod."},{"key":"ref_15","unstructured":"Zangerl, F., Griesauer, F., Sust, M., Montenbruck, O., Buchert, B., and Garcia, A. (2014, January 8\u201312). SWARM GPS Precise Orbit Determination Receiver Initial in-Orbit Performance Evaluation. Proceedings of the 27th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+), Tampa, FL, USA."},{"key":"ref_16","unstructured":"F\u00f6rste, C., and Bruinsma, S.L. EIGEN-6S4: A Time-Variable Satellite-Only Gravity Field Model to d\/o 300 Based on LAGEOS, GRACE and GOCE Data from the Collaboration of GFZ Potsdam and GRGS Toulouse. Available online: http:\/\/doi.org\/10.5880\/icgem.2016.008."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.5047\/eps.2013.07.001","article-title":"The Swarm Satellite Constellation Application and Research Facility (SCARF) and Swarm data products","volume":"65","author":"Olsen","year":"2013","journal-title":"Earth Planets Space"},{"key":"ref_18","first-page":"1405","article-title":"Precise orbit determination for CHAMP using accelerometer data","volume":"112","author":"Kang","year":"2002","journal-title":"Adv. Astronaut. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1007\/s11434-008-0513-0","article-title":"Precise orbit determination for Jason-1 satellite using on-board GPS data with cm-level accuracy","volume":"54","author":"Peng","year":"2009","journal-title":"Chin. Sci. Bull."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.asr.2005.04.066","article-title":"Kinematic positioning of LEO and GPS satellites and IGS stations on the ground","volume":"36","author":"Rothacher","year":"2005","journal-title":"Adv. Space Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"24","DOI":"10.2514\/3.20600","article-title":"Reduced-dynamic technique for precise orbit determination of low earth satellites","volume":"14","author":"Wu","year":"1991","journal-title":"J. Guid."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s00190-006-0029-9","article-title":"Pseudo-stochastic orbit modeling technique for low Earth orbiters","volume":"80","author":"Hugentobler","year":"2006","journal-title":"J. Geod."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.ast.2005.01.003","article-title":"Reduced dynamic orbit determination using GPS code and carrier measurements","volume":"9","author":"Montenbruck","year":"2005","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s00190-006-0072-6","article-title":"Efficient satellite orbit modeling using pseudo-stochastic parameters","volume":"80","author":"Beutler","year":"2006","journal-title":"J. Geod."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Beutler, G. (2004). Methods of Celestial Mechanics, Springer.","DOI":"10.1007\/b137725"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2024","DOI":"10.1007\/s11434-007-0264-3","article-title":"Zero-difference and single-difference precise orbit determination for LEO using GPS","volume":"52","author":"Peng","year":"2007","journal-title":"Chin. Sci. Bull."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/s00190-010-0401-7","article-title":"The celestial mechanics approach: Theoretical foundations","volume":"84","author":"Beutler","year":"2010","journal-title":"J. Geod."},{"key":"ref_28","unstructured":"Standish, E.M. (1998). JPL Planetary and Lunar Ephemerides, DE405\/LE405, JPL. JPL IOM 312.F-98-048."},{"key":"ref_29","unstructured":"Petit, G., and Luzum, B. (2010). IERS Conventions 2010, Verlag des Bundesamts f\u00fcr Kartographie und Geod\u00e4sie. IERS Technical Note."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1007\/s10236-006-0086-x","article-title":"Modelling the global ocean tides: Insights from FES2004","volume":"56","author":"Lyard","year":"2006","journal-title":"Ocean Dyn."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1007\/s00190-009-0326-1","article-title":"High-rate GPS clock corrections from CODE: Support of 1 Hz applications","volume":"83","author":"Bock","year":"2009","journal-title":"J. Geod."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s00190-008-0281-2","article-title":"GNSS processing at CODE: Status report","volume":"83","author":"Dach","year":"2009","journal-title":"J. Geod."},{"key":"ref_33","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_34","unstructured":"Dach, R., Lutz, S., Walser, P., and Fridez, P. (2015). Bernese GNSS Software Version 5.2, Astronomical Institute, University of Bern, Bern Open Publishing. User Manual."},{"key":"ref_35","unstructured":"\u0160vehla, D., and Rothacher, M. (2003). EGS-AGU-EUG Nice Kinematic and Reduced-Dynamic Precise Orbit Determination of CHAMP Satellite over One Year Using Space-Borne GPS Phase Zero-Differences Only, EGS-AGU-EUG Joint Assembly."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/635\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:30:52Z","timestamp":1760207452000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/635"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,20]]},"references-count":35,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["s17030635"],"URL":"https:\/\/doi.org\/10.3390\/s17030635","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,3,20]]}}}