{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:41:50Z","timestamp":1760240510810,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2019,7,5]],"date-time":"2019-07-05T00:00:00Z","timestamp":1562284800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2018YFC1505102"],"award-info":[{"award-number":["2018YFC1505102"]}]},{"name":"the Programs of the National Natural Science Foundation of China","award":["41774025, 41731066"],"award-info":[{"award-number":["41774025, 41731066"]}]},{"name":"the Special Fund for Technological Innovation Guidance of Shaanxi Province","award":["2018XNCGG05"],"award-info":[{"award-number":["2018XNCGG05"]}]},{"name":"the Special Fund for Basic Scientific Research of Central Colleges","award":["CHD300102269305, CHD300102268305"],"award-info":[{"award-number":["CHD300102269305, CHD300102268305"]}]},{"name":"the Grand Projects of the Beidou-2 System","award":["GFZX0301040308"],"award-info":[{"award-number":["GFZX0301040308"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Due to the cuboid satellite body of BeiDou-3 satellites, the accuracy of their orbit showed a trend of systematic variation with the sun-satellite-earth angle (\u03b5) using the Extend CODE Orbit Model (ECOM1). Therefore, an a priori cuboid box-wing model (named the cuboid model) is necessary to compensate ECOM1. Considering that the body-dimensions and optical properties of the BeiDou-3 satellites used to construct the box-wing model have not yet been fully released, the adjustable box-wing model (ABW) was used for precise orbit determination (POD). The a priori cuboid box-wing model was directly estimated by the precision radiation accelerations, obtained from ABW POD. When using ECOM1 model, for 14 &lt; \u03b2 &lt; 40\u00b0, a linear systematic variation of D0 related to the elevation of the sun above the orbital plane (\u03b2-angle) with a slope of 0.048 nm\/s2\/\u00b0, was found for C30. After adding the cuboid model to assist ECOM1 (named Cuboid + ECOM1), the slope was reduced to 0.005 nm\/s2\/\u00b0, and for C20 satellite, the standard deviation (STD) of D0 was improved, from 1.28 to 0.85 nm\/s2 (34%). For satellite laser ranging (SLR) validation, when using the ECOM1 model, the systematic variation with the \u03b5 angle was about 14 cm for C20 and C30. After using the Cuboid + ECOM1 model, the variation was significantly reduced to about 5 cm. For C20 and C21, compared with the ECOM1 model, the root mean square (RMS) of the ECOM2 and Cuboid + ECOM1 model was improved by about 0.54 (10.3%) and 0.43 cm (8.7%). For C29 and C30, the RMS of ECOM2 and Cuboid + ECOM1 model was improved for about 0.7 (10.9%) and 1.6 cm (25.6%). Finally, the RMS of the SLR residuals of 4.37 to 4.88 cm was achieved for BeiDou-3 POD.<\/jats:p>","DOI":"10.3390\/rs11131605","type":"journal-article","created":{"date-parts":[[2019,7,5]],"date-time":"2019-07-05T11:44:16Z","timestamp":1562327056000},"page":"1605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["A Priori Solar Radiation Pressure Model for BeiDou-3 MEO Satellites"],"prefix":"10.3390","volume":"11","author":[{"given":"Xingyuan","family":"Yan","sequence":"first","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}]},{"given":"Chenchen","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}]},{"given":"Guanwen","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}]},{"given":"Qin","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}]},{"given":"Le","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7387-5110","authenticated-orcid":false,"given":"Zhiwei","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}]},{"given":"Shichao","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,5]]},"reference":[{"key":"ref_1","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":"2018","journal-title":"GPS Solut."},{"key":"ref_2","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_3","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":"Manuscripta Geodaetica"},{"key":"ref_4","unstructured":"Deng, Z., Fritsche, M., Uhlemann, M., Wickert, J., and Schuh, H. (2016, January 8\u201312). Reprocessing of GFZ Multi-GNSS Product GBM. Proceedings of the IGS Workshop 2016, Sydney, Australia."},{"key":"ref_5","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)\u2013achievements, prospects and challenges","volume":"59","author":"Montenbruck","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s00190-014-0774-0","article-title":"Enhanced solar radiation pressure modeling for Galileo satellites","volume":"89","author":"Montenbruck","year":"2015","journal-title":"J. Geod."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1007\/s00190-015-0814-4","article-title":"CODE\u2019s new solar radiation pressure model for GNSS orbit determination","volume":"89","author":"Arnold","year":"2015","journal-title":"J. Geod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s00190-016-0968-8","article-title":"CODE\u2019s five-system orbit and clock solution the challenges of multi-GNSS data analysis","volume":"91","author":"Prange","year":"2017","journal-title":"J. Geod."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s10291-016-0566-5","article-title":"Galileo status: Orbits, clocks, and positioning","volume":"21","author":"Steigenberger","year":"2016","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2088","DOI":"10.1016\/j.asr.2017.01.036","article-title":"Semi-analytical solar radiation pressure modeling for QZS-1 orbit-normal and yaw-steering attitude","volume":"59","author":"Montenbruck","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s00190-017-1048-4","article-title":"An a priori solar radiation pressure model for the QZSS Michibiki satellite","volume":"92","author":"Zhao","year":"2018","journal-title":"J. Geod."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1007\/s00190-018-1199-y","article-title":"Empirically derived model of solar radiation pressure for BeiDou GEO satellites","volume":"93","author":"Wang","year":"2019","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wang, C., Guo, J., Zhao, Q., and Liu, J. (2018). Solar Radiation Pressure Models for BeiDou-3 I2-S Satellite: Comparison and Augmentation. Remote Sens., 10.","DOI":"10.3390\/rs10010118"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1016\/j.asr.2012.01.016","article-title":"Adjustable box-wing model for solar radiation pressure impacting GPS satellites","volume":"49","author":"Hugentobler","year":"2012","journal-title":"Adv. Space Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1016\/j.asr.2013.07.013","article-title":"Improving the orbits of GPS block IIA satellites during eclipse seasons","volume":"52","author":"Hugentobler","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.1016\/j.asr.2018.11.007","article-title":"The Adjusted Optical Properties for Galileo\/BeiDou-2\/QZS-1 Satellites and Initial Results on BeiDou-3e and QZS-2 satellites","volume":"63","author":"Duan","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1007\/s10291-019-0860-0","article-title":"Accounting for perturbing forces acting on Galileo using a box-wing model","volume":"23","author":"Bury","year":"2019","journal-title":"GPS Solut."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1016\/j.asr.2018.10.038","article-title":"Early analysis of precise orbit and clock offset determination for the satellites of the global BeiDou-3 system","volume":"63","author":"Yan","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_19","unstructured":"Xia, L., Baojun, L., Yingchun, L., Sujie, X., and Tao, B. (2018). Satellite Geometry and Attitude Mode of MEO Satellites of BDS-3 Developed by SECM, ION GNSS+."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s10291-016-0540-2","article-title":"Comparison of solar radiation pressure models for BDS IGSO and MEO satellites with emphasis on improving orbit quality","volume":"21","author":"Guo","year":"2017","journal-title":"GPS Solut."},{"key":"ref_21","unstructured":"Dilssner, F. (2019, February 20). A Note on the Yaw Attitude Modeling of BeiDou IGSO-6, a Report Dated November 20, 2017. Available online: http:\/\/navigation-office.esa.int\/attachments_24576369_1_BeiDou_IGSO-6_Yaw_Modeling.pdf."},{"key":"ref_22","unstructured":"Milani, A., Nobili, A.M., and Farinella, P. (1987). Non-Gravitational Perturbations and Satellite Geodesy, Adam Hilger."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1007\/s00190-009-0315-4","article-title":"The international GNSS service in a changing landscape of global navigation satellite systems","volume":"83","author":"Dow","year":"2009","journal-title":"J. Geod."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s00190-015-0862-9","article-title":"Precise orbit determination for Quad-constellation satellites at Wuhan University: Strategy, result validation, and comparison","volume":"90","author":"Guo","year":"2016","journal-title":"J. Geod."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1016\/j.asr.2015.06.019","article-title":"GNSS satellite geometry and attitude models","volume":"56","author":"Montenbruck","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s00190-015-0829-x","article-title":"Estimating the yaw-attitude of BDS IGSO and MEO satellites","volume":"89","author":"Dai","year":"2015","journal-title":"J. Geod."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02521844","article-title":"Contributions to the theory of atmospheric refraction, part II: Refraction corrections in satellite Geodesy","volume":"105","author":"Saastamoinen","year":"1973","journal-title":"Bull. Geod."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"L07304","DOI":"10.1029\/2005GL025546","article-title":"Global Mapping Function (GMF): A New Empirical Mapping Function Based on Numerical Weather Model Data","volume":"33","author":"Boehm","year":"2006","journal-title":"Geophy. Res. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.asr.2018.05.021","article-title":"Impact of BDS-3 experimental satellites to BDS-2: Service area, precise products, precise positioning","volume":"62","author":"Zhang","year":"2018","journal-title":"Adv. Space Res."},{"key":"ref_30","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_31","unstructured":"Urschl, C., Beutler, G., Gurtner, W., Hugentobler, U., and Ploner, M. Orbit determination for GIOVE-A using SLR tracking data. Extending the Range, Proceedings of the 15th International Workshop on Laser Ranging, Canberra, Australia, 15\u201320 October 2006, Available online: http:\/\/cddis.gsfc.nasa.gov\/lw15\/docs\/papers\/Orbit%20Determination%20for%20GIOVE-A%20using%20SLR%20Tracking%20Data.pdf."},{"key":"ref_32","unstructured":"Pavlis, E. (2009, January 22\u201324). SLRF2008: The ILRS reference frame for SLR POD contributed to ITRF2008. Proceedings of the 2009 Ocean Surface Topography Science Team Meeting, Seattle, WA, USA."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s10291-018-0716-z","article-title":"Estimation of antenna phase center offset for BDS IGSO and MEO satellites","volume":"22","author":"Huang","year":"2018","journal-title":"GPS Solut."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1007\/s00190-016-0909-6","article-title":"Estimation of satellite antenna phase center offsets for galileo","volume":"90","author":"Steigenberger","year":"2016","journal-title":"J. Geod."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/13\/1605\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:03:03Z","timestamp":1760187783000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/13\/1605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,5]]},"references-count":34,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["rs11131605"],"URL":"https:\/\/doi.org\/10.3390\/rs11131605","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2019,7,5]]}}}