{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T09:36:27Z","timestamp":1769938587302,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,11,21]],"date-time":"2019-11-21T00:00:00Z","timestamp":1574294400000},"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>The BeiDou Navigation Satellite System (BDS) of China is currently in the hybrid-use period of BDS-2 and BDS-3 satellites. All of them are equipped with Laser Retroreflect Arrays (LRAs) for Satellite Laser Ranging (SLR), which can directly obtain an independent, sub-centimetre level of distance measurement. The main purpose of this contribution is to use the solely SLR Normal Points (NPs) data to determinate the precise orbit of BDS-2 and BDS-3 satellites, including one Geostationary Earth Orbit (GEO), three Inclined Geo-Synchronous Orbits (ISGO), and one Medium Earth Orbit (MEO) of BDS-2 satellites, as well as four MEO of BDS-3 satellites, from 1 January to 30 June 2019. The microwave-based orbit from Wuhan University (WUM) are firstly validated to mark and eliminate the bad SLR observations in our preprocessing stage. Then, the 3-, 5-, 7-, and 9-day arc solutions are performed to investigate the impact of the different orbital arc lengths on the quality of SLR-derived orbits and test the optimal solution of the multi-day arc. Moreover, the dependency of SLR-only orbit determination accuracy on the number of SLR observations and the number of SLR sites are discussed to explore the orbit determination quality of the 3-,5-, 7-, and 9-day arc solutions. The results indicate that (1) during the half-year time span of 2019, the overall Root Mean Square (RMS) of SLR validation residuals derived from WUM is 19.0 cm for BDS-2 GEO C01, 5.2\u20137.3 cm for three BDS-2 IGSO, 3.4 cm for BDS-2 MEO C11, and 4.4\u20135.7 cm for four BDS-3 MEO satellites respectively. (2) The 9-day arc solutions present the best orbit accuracy in our multi-day SLR-only orbit determination for BDS IGSO and MEO satellites. The 9-day overlaps median RMS of BDS MEO in RTN directions are evaluated at 3.6\u20135.7, 12.4\u201321.6, and 15.6\u201323.9 cm respectively, as well as 5.7\u20139.6, 15.0\u201336.8, and 16.5\u201335.2 cm for the comparison with WUM precise orbits, while these values of BDS IGSO are larger by a factor of about 3\u201310 than BDS MEO orbits in their corresponding RTN directions. Furthermore, the optimal average 3D-RMS of 9-day overlaps is 0.49 and 1.89 m for BDS MEO and IGSO respectively, as well as 0.55 and 1.85 m in comparison with WUM orbits. Owing to its extremely rare SLR observations, the SLR-only orbit determination accuracy of BDS-2 GEO satellite can only reach a level of 10 metres or worse. (3) To obtain a stable and reliable SLR-only precise orbit, the 7-day to 9-day arc solutions are necessary to provide a sufficient SLR observation quantity and geometry, with more than 50\u201380 available SLR observations at 5\u20136 SLR sites that are evenly distributed, both in the Northern and Southern Hemispheres.<\/jats:p>","DOI":"10.3390\/rs11232735","type":"journal-article","created":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T02:49:27Z","timestamp":1574390967000},"page":"2735","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Precise Orbit Determination of BDS-2 and BDS-3 Using SLR"],"prefix":"10.3390","volume":"11","author":[{"given":"Honglei","family":"Yang","sequence":"first","affiliation":[{"name":"Institute of Space Science, Shandong University, Weihai 264209, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5818-6264","authenticated-orcid":false,"given":"Tianhe","family":"Xu","sequence":"additional","affiliation":[{"name":"Institute of Space Science, Shandong University, Weihai 264209, China"}]},{"given":"Wenfeng","family":"Nie","sequence":"additional","affiliation":[{"name":"Institute of Space Science, Shandong University, Weihai 264209, China"}]},{"given":"Fan","family":"Gao","sequence":"additional","affiliation":[{"name":"Institute of Space Science, Shandong University, Weihai 264209, China"}]},{"given":"Meiqian","family":"Guan","sequence":"additional","affiliation":[{"name":"Institute of Space Science, Shandong University, Weihai 264209, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1007\/s11430-017-9186-9","article-title":"Progress and performance evaluation of BeiDou global navigation satellite system: Data analysis based on BDS-3 demonstration system","volume":"61","author":"Yang","year":"2018","journal-title":"Sci. China Earth Sci."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yang, Y., Gao, W., Guo, S., Mao, Y., and Yang, Y. (2019). Introduction to BeiDou-3 navigation satellite system. Navigation, 66.","DOI":"10.1002\/navi.291"},{"key":"ref_3","first-page":"62","article-title":"Laser Ranging to GPS Satellites with Centimeter Accuracy","volume":"1994","author":"Degnan","year":"1994","journal-title":"GPS World"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0273-1177(95)98780-R","article-title":"Comparison of GPS S\/C orbits determined from GPS and SLR tracking data","volume":"16","author":"Pavlis","year":"1995","journal-title":"Adv. Space Res."},{"key":"ref_5","unstructured":"Schutz, B.E. (1994, January 1\u20132). Synergism of SLR and GPS. Proceedings of the Satellite Laser Ranging in the 1990s: Report of the 1994 Belmont Workshop, Elkridge, MD, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s001900050110","article-title":"Apropos laser tracking to GPS satellites","volume":"71","author":"Zhu","year":"1997","journal-title":"J. Geod."},{"key":"ref_7","unstructured":"Eanes, R.J., Nerem, R.S., Abusali, P.A.M., Bamford, W., and Ries, J.C. (1999). GLONASS Orbit Determination at the Center for Space Research, University of Texas at Austin."},{"key":"ref_8","unstructured":"Melachroinos, S.A., Perosanz, F., Deleflie, F., Biancalel, R., Laurain, O., and Exertier, P. (2006, January 15\u201320). GIOVE-A and GPS-35\/36 orbit determination and analysis of dynamical properties based on SLR-only tracking data. Proceedings of the 15th International Workshop on Laser Ranging, Canberra, Australia."},{"key":"ref_9","unstructured":"Schonemann, E., Springer, T., Otten, M., Becker, M., and Dow, J. (2007, January 1\u20134). GIOVE-A precise orbit determination from microwave and satellite laser ranging data\u2014first perspectives for the Galileo constellation and its scientific use. Proceedings of the First Colloquium on Scientific and Fundamental Aspects of the Galileo Programme, Toulouse, France. Available online: http:\/\/ilrs.gsfc.nasa.gov\/docs\/2007_Schoenemann_Toulouse_paper.pdf."},{"key":"ref_10","unstructured":"Urschl, C., Beutler, G., Gurtner, W., Hugentober, U., and Ploner, M. (2006, January 15\u201320). Orbit determination for GIOVE-A using SLR tracking data. Proceedings of the 15th International Workshop on Laser Ranging, Canberra, Australia."},{"key":"ref_11","unstructured":"Flohrer, C. (2008). Mutual Validation of Satellite-Geodetic Techniques and its Impact on GNSS Orbit Modeling, Swiss Geodetic Commission. Geod\u00e4tisch-geophysikalische Arbeiten in der Schweiz."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhao, G., Zhou, S.S., Zhou, X.H., and Wu, B. (2013). Precise Orbit Determination of BeiDou Satellites Using Satellite Laser Ranging, Springer.","DOI":"10.1007\/978-3-642-37407-4_20"},{"key":"ref_13","unstructured":"Zhao, G., Zhou, S.S., Zhou, X.H., and Wu, B. (2013, January 1\u20133). Comparison on orbit precisions of different types of navigation satellites based on SLR tracking data. Proceedings of the 18th International Workshop on Laser Ranging, Goar, Germany."},{"key":"ref_14","unstructured":"Bury, G., So\u015bnica, K., and Zajdel, R. (2017, January 2\u20135). How many SLR observations and how many stations are needed for deriving high-quality multi-GNSS orbits?. Proceedings of the 2017 ILRS Technical Workshop, Riga, Latvia."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bury, G., So\u015bnica, K., and Zajdel, R. (2019). Multi-GNSS orbit determination using satellite laser ranging. J. Geod., 1\u201317.","DOI":"10.1007\/s00190-018-1143-1"},{"key":"ref_16","first-page":"367","article-title":"Extended orbit modeling techniques at the CODE processing center of the International GPS Service for geodynamics (IGS): Theory and initial results","volume":"19","author":"Beutler","year":"1994","journal-title":"Manuscr. Geod."},{"key":"ref_17","first-page":"252","article-title":"The observational basis for JPL\u2019s DE 200, the planetary ephemerides of the Astronomical Almanac","volume":"233","author":"Standish","year":"1990","journal-title":"Astron. Astrophys."},{"key":"ref_18","unstructured":"Petit, G., and Luzum, B. (2010). IERS Conventions. (IERS Technical Note; No. 36) Frankfurt am Main: Verlag des Bundesamts f\u00fcr Kartographie und Geod\u00e4sie, IERS Technical Note."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1029\/2004GL020308","article-title":"High-accuracy zenith delay prediction at optical wavelengths","volume":"31","author":"Mendes","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.asr.2019.04.030","article-title":"SLR validation and evaluation on BDS precise orbits from 2013 to 2018","volume":"64","author":"Yang","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_21","unstructured":"Dach, R., Lutz, S., Walser, P., and Fridez, P. (2015). Bernese GNSS Software Version 5.2, University of Bern, Bern Open Publishing."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/BF00867349","article-title":"Combining consecutive short arcs into long arcs for precise and efficient GPS Orbit Determination","volume":"70","author":"Beutler","year":"1996","journal-title":"J. Geod."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s00190-015-0878-1","article-title":"Impact of the arc length on GNSS analysis results","volume":"90","author":"Lutz","year":"2016","journal-title":"J. Geod."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00190-016-0968-8","article-title":"CODE\u2019s five-system orbit and clock solution\u2014The challenges of multi-GNSS data analysis","volume":"91","author":"Prange","year":"2017","journal-title":"J. Geod."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.asr.2005.03.021","article-title":"Validation of GNSS orbits using SLR observations","volume":"36","author":"Urschl","year":"2005","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1016\/j.asr.2007.01.038","article-title":"Contribution of SLR tracking data to GNSS orbit determination","volume":"39","author":"Urschl","year":"2007","journal-title":"Adv. Space Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1007\/s00190-015-0810-8","article-title":"Satellite laser ranging to GPS and GLONASS","volume":"89","author":"Thaller","year":"2015","journal-title":"J Geod."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Yang, H., Xu, T., and Sun, D. (2016). Validation of GPS36 Satellite CODE Precise Orbit with SLR Measurements, Springer. China Satellite Navigation Conference (CSNC) 2016 Proceedings: Volume III, Lecture Notes in Electrical Engineering 390.","DOI":"10.1007\/978-981-10-0940-2_13"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s00190-017-1050-x","article-title":"Validation of Galileo orbits using SLR with a focus on satellites launched into incorrect orbital planes","volume":"92","author":"Prange","year":"2018","journal-title":"J. Geod."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zajdel, R., So\u015bnica, K., and Bury, G. (2017). A New Online Service for the Validation of Multi-GNSS Orbits Using SLR. Remote Sens., 9.","DOI":"10.3390\/rs9101049"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s10291-017-0673-y","article-title":"Precise orbit and clock determination for BeiDou-3 experimental satellites with yaw attitude analysis","volume":"22","author":"Zhao","year":"2017","journal-title":"GPS Solut."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s10291-018-0783-1","article-title":"Yaw attitude modeling for BeiDou I06 and BeiDou-3 satellites","volume":"22","author":"Wang","year":"2018","journal-title":"GPS Solut."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/23\/2735\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:36:18Z","timestamp":1760189778000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/23\/2735"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,21]]},"references-count":32,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["rs11232735"],"URL":"https:\/\/doi.org\/10.3390\/rs11232735","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,21]]}}}