{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T19:47:01Z","timestamp":1772826421305,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,17]],"date-time":"2021-01-17T00:00:00Z","timestamp":1610841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2016YFC0803109"],"award-info":[{"award-number":["2016YFC0803109"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hebei Ecological Intelligent Mine Joint Foundation","award":["E2020402086"],"award-info":[{"award-number":["E2020402086"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41772130"],"award-info":[{"award-number":["41772130"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Anhui University of Science and Technology Graduate Innovation Foundation","award":["2019CX2077"],"award-info":[{"award-number":["2019CX2077"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The BeiDou Navigation Satellite System (BDS) features a heterogeneous constellation so that it is difficult to mitigate the multipath in the coordinate-domain. Therefore, mitigating the multipath in the observation-domain becomes more important. Sidereal filtering is commonly used for multipath mitigation, which needs to calculate the orbit repeat time of each satellite. However, that poses a computational challenge and damages the integrity at the end of the multipath model. Therefore, this paper proposes a single-difference model based on the multipath hemispherical map (SD-MHM) to mitigate the BDS-2\/BDS-3 multipath in a short baseline. The proposed method is converted from double-difference residuals to single-difference residuals, which is not restricted by the pivot satellite transformation. Moreover, it takes the elevation and the azimuth angles of the satellite as the independent variables of the multipath model. The SD-MHM overcomes the unequal observation time of some satellites and does not require specific hardware. The experimental results show that the SD-MHM reduces the root mean square of the positioning errors by 56.4%, 63.9%, and 67.4% in the east, north, and vertical directions; moreover, it contributes to an increase in the baseline accuracy from 1.97 to 0.84 mm. The proposed SD-MHM has significant advantages in multipath mitigation compared with the advanced sidereal filtering method. Besides, the SD-MHM also features an excellent multipath correction capability for observation data with a period of more than seven days. Therefore, the SD-MHM provides a universal strategy for BDS multipath mitigation.<\/jats:p>","DOI":"10.3390\/rs13020304","type":"journal-article","created":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T03:34:25Z","timestamp":1611113665000},"page":"304","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A Single-Difference Multipath Hemispherical Map for Multipath Mitigation in BDS-2\/BDS-3 Short Baseline Positioning"],"prefix":"10.3390","volume":"13","author":[{"given":"Chao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Spatial Information and Geomatics Engineering, Anhui University of Science and Technology, Huainan 232001, China"},{"name":"School of Mining and Geomatics, Hebei University of Engineering, Handan 056038, China"},{"name":"Jiangsu Key Laboratory of Resources and Environmental Information Engineering, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Tao","sequence":"additional","affiliation":[{"name":"School of Spatial Information and Geomatics Engineering, Anhui University of Science and Technology, Huainan 232001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiqiang","family":"Xin","sequence":"additional","affiliation":[{"name":"Xinjiang Academy of Surveying and Mapping, Urumqi 830002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingwang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Spatial Information and Geomatics Engineering, Anhui University of Science and Technology, Huainan 232001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunyang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Spatial Information and Geomatics Engineering, Anhui University of Science and Technology, Huainan 232001, China"},{"name":"Jiangsu Key Laboratory of Resources and Environmental Information Engineering, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haojie","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Spatial Information and Geomatics Engineering, Anhui University of Science and Technology, Huainan 232001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tengfei","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1002\/navi.291","article-title":"Introduction to BeiDou-3 navigation satellite system","volume":"66","author":"Yang","year":"2019","journal-title":"Navigation"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"108231","DOI":"10.1016\/j.measurement.2020.108231","article-title":"Investigation of real-time kinematic multi-GNSS precise point positioning with the CNES products","volume":"166","author":"Zhao","year":"2020","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1007\/s10291-019-0928-x","article-title":"Initial assessment of BDS-3 preliminary system signal-in-space range error","volume":"24","author":"Lv","year":"2020","journal-title":"GPS Solut."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108237","DOI":"10.1016\/j.measurement.2020.108237","article-title":"Investigation of real-time carrier phase time transfer using current multi-constellations","volume":"166","author":"Wang","year":"2020","journal-title":"Measurement"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.measurement.2018.02.001","article-title":"Bridge monitoring using BDS-RTK and GPS-RTK techniques","volume":"120","author":"Xi","year":"2018","journal-title":"Measurement"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s10291-019-0847-x","article-title":"Performance of BDS-3: Satellite visibility and dilution of precision","volume":"23","author":"Wang","year":"2019","journal-title":"GPS Solut."},{"key":"ref_7","first-page":"109","article-title":"Multipath mitigation under forest canopies: A choke ring antenna solution","volume":"55","author":"Danskin","year":"2009","journal-title":"For. 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