{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T15:44:09Z","timestamp":1784389449537,"version":"3.55.0"},"reference-count":38,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,17]],"date-time":"2021-07-17T00:00:00Z","timestamp":1626480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shanghai Nature Science Fund","award":["19ZR1426800"],"award-info":[{"award-number":["19ZR1426800"]}]},{"name":"Shanghai Jiao Tong University Global Strategic Partnership Fund","award":["2019 SJTU-UoT, WF610561702"],"award-info":[{"award-number":["2019 SJTU-UoT, WF610561702"]}]},{"name":"Shanghai Jiao Tong University Young Teachers Initiation Programme","award":["AF4130045"],"award-info":[{"award-number":["AF4130045"]}]},{"name":"National Key R&amp;D Program of China","award":["2020YFC2200800"],"award-info":[{"award-number":["2020YFC2200800"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U20B2054"],"award-info":[{"award-number":["U20B2054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U20B2056"],"award-info":[{"award-number":["U20B2056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this study, submillimeter level accuracy K-band microwave ranging (MWR) equipment is demonstrated, aiming to verify the detection of the Earth\u2019s gravity field (EGF) and digital elevation models (DEM), through spacecraft formation flying (SFF) in low Earth orbit (LEO). In particular, this paper introduces in detail an integrated BeiDou III B1C\/B2a dual frequency receiver we designed and developed, including signal processing scheme, gain allocation, and frequency planning. The receiver matched the 0.1 ns precise synchronize time-frequency benchmark for the MWR system, verified by a static and dynamic test, compared with a time interval counter synchronization solution. Moreover, MWR equipment ranging accuracy is explored in-depth by using different ranging techniques. The test results show that MWR achieved 40 \u03bcm and 1.6 \u03bcm\/s accuracy for ranging and range rate during tests, using synchronous dual one-way ranging (DOWR) microwave phase accumulation frame, and 6 \u03bcm\/s range rate accuracy obtained through a one-way ranging experiment. The ranging error sources of the whole MWR system in-orbit are analyzed, while the relative orbit dynamic models, for formation scenes, and adaptive Kalman filter algorithms, for SFF relative navigation designs, are introduced. The performance of SFF relative navigation using MWR are tested in a hardware in loop (HIL) simulation system within a high precision six degree of freedom (6-DOF) moving platform. The final estimation error from adaptive relative navigation system using MWR are about 0.42 mm (range\/RMS) and 0.87 \u03bcm\/s (range rate\/RMS), which demonstrated the promising accuracy for future applications of EGF and DEM formation missions in space.<\/jats:p>","DOI":"10.3390\/s21144883","type":"journal-article","created":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T21:18:52Z","timestamp":1626643132000},"page":"4883","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Evaluation of Precise Microwave Ranging Technology for Low Earth Orbit Formation Missions with Beidou Time-Synchronize Receiver"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4345-1613","authenticated-orcid":false,"given":"Xiaoliang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shufan","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Deren","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiang","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dengfeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Space Radio Technology, Xi\u2019an 710100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher","family":"Damaren","sequence":"additional","affiliation":[{"name":"Institute for Aerospace Studies, University of Toronto, Toronto, ON M1C 1A4, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,17]]},"reference":[{"key":"ref_1","unstructured":"Alfriend, K., Vadali, S.R., Gurfil, P., How, J., and Breger, L. 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