{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:32:08Z","timestamp":1760401928254,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,4,19]],"date-time":"2020-04-19T00:00:00Z","timestamp":1587254400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.61671264"],"award-info":[{"award-number":["No.61671264"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To maximize the usage of limited transmission power and wireless spectrum, more communication satellites are adopting precise space\u2013ground beam-forming, which poses a rigorous positioning and timing requirement of the satellite. To fulfill this requirement, a space-borne global navigation satellite system (GNSS) timing receiver with a disciplined high-performance clock is preferable. The space-borne GNSS timing receiver moves with the satellite, in contrast to its stationary counterpart on ground, making it tricky in its positioning algorithm design. Despite abundant existing positioning algorithms, there is a lack of dedicated work that systematically describes the delicate aspects of a space-borne GNSS timing receiver. Based on the experimental work of the LING QIAO (NORAD ID:40136) communication satellite\u2019s GNSS receiver, we propose a fine-tuned positioning algorithm for space-borne GNSS timing receivers. Specifically, the proposed algorithm includes: (1) a filtering architecture that separates the estimation of satellite position and velocity from other unknowns, which allows for a first estimation of satellite position and velocity incorporating any variation of orbit dynamics; (2) a two-threshold robust cubature Kalman filter to counteract the adverse influence of measurement outliers on positioning quality; (3) Reynolds averaging inspired clock and frequency error estimation. Hardware emulation test results show that the proposed algorithm has a performance with a 3D positioning RMS error of 1.2 m, 3D velocity RMS error of 0.02 m\/s and a pulse per second (PPS) RMS error of 11.8ns. Simulations with MATLAB show that it can effectively detect and dispose outliers, and further on outperforms other algorithms in comparison.<\/jats:p>","DOI":"10.3390\/s20082327","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T04:49:38Z","timestamp":1587444578000},"page":"2327","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Fine-Tuned Positioning Algorithm for Space-Borne GNSS Timing Receivers"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3671-6425","authenticated-orcid":false,"given":"Xi","family":"Chen","sequence":"first","affiliation":[{"name":"National Research Institute of Information Science and Technologies, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3447-4629","authenticated-orcid":false,"given":"QiHui","family":"Wei","sequence":"additional","affiliation":[{"name":"National Research Institute of Information Science and Technologies, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YaFeng","family":"Zhan","sequence":"additional","affiliation":[{"name":"National Research Institute of Information Science and Technologies, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TianYi","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,19]]},"reference":[{"key":"ref_1","unstructured":"Stieglitz, J.L. (1999, January 24\u201329). Global Positioning System receivers in space applications. Proceedings of the 18th Digital Avionics Systems Conference, St Louis, MO, USA."},{"key":"ref_2","unstructured":"Bertiger, W., Haines, B., Kuang, D., Lough, M., Lichten, S., Muellerschoen, R., Vigue-Rodi, Y., and Wu, S. (1999). Precise Real-Time Low-Earth-Orbiter Navigation With the Global Positioning System (GPS)."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Abbas, N.N., Li, Y.J., and Fiaz, M. (2013, January 27\u201330). Attitude Determination of small satellite using phase and code measurements of Global Navigation Satellite System: Design, simulation and comparison. Proceedings of the Electronics, Communications and Photonics Conference, Fira, Greece.","DOI":"10.1109\/SIECPC.2013.6550795"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1109\/JSTARS.2014.2303251","article-title":"Precision bounds in GNSS-R ocean altimetry","volume":"7","author":"Pascual","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Fazliani, Y., Unwin, M., and Jales, P. (2012, January 5\u20137). Satellite-borne remote sensing: Using Space GPS\/GNSS receiver for reflectometry. Proceedings of the Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing, Noordwijk, The Netherlands.","DOI":"10.1109\/NAVITEC.2012.6423102"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4771","DOI":"10.1109\/JSTARS.2016.2565687","article-title":"Vegetation Sensing Using GPS Interferometric Reflectometry: Experimental Results With a Horizontally Polarized Antenna","volume":"9","author":"Chen","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Purivigraipong, S., and Kuntanapreeda, S. (2005, January 21\u201324). Spacecraft Orbit Determination from Code Informtation of Global Positioning System Signals. Proceedings of the TENCON 2005, Melbourne, Australia.","DOI":"10.1109\/TENCON.2005.300830"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tsui, J.B.Y. (2004). Fundamentals of Global Positioning System Receivers: A Software Approach, John Wiley & Sons Inc.. [2nd ed.].","DOI":"10.1002\/0471712582"},{"key":"ref_9","unstructured":"Misra, P., and Enge, P. (2006). Global Positioning System: Signals, Measurements, and Performance, Ganga-Jamuna Press. [2nd ed.]."},{"key":"ref_10","unstructured":"Kaplan, E.D., and Hegarty, C. (2005). Understanding GPS: Principles and Applications, Artech House. [2nd ed.]."},{"key":"ref_11","unstructured":"Wan, E., and Merwe, R. (2000, January 4). The Unscented Kalman Filter for Nonlinear Estimation. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium, Lake Louise, AB, Canada."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhai, X., Qi, F., Zhang, H., and Xu, H. (2012, January 21\u201323). Application of unscented Kalman filter in GPS\/INS. Proceedings of the Photonics and Optoelectronics, Shanghai, China.","DOI":"10.1109\/SOPO.2012.6270470"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","article-title":"Cubature Kalman Filters","volume":"54","author":"Arasaratnam","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1002\/asjc.926","article-title":"A New Derivation of the Cubature Kalman Filters","volume":"16","author":"Zhang","year":"2015","journal-title":"Asian J. Control"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Pesonen, H., and Piche, R. (2010, January 11\u201312). Cubature-based Kalman filters for positioning. Proceedings of the Positioning Navigation and Communication, Dresden, Germany.","DOI":"10.1109\/WPNC.2010.5653829"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1049\/iet-rsn.2012.0170","article-title":"Adaptive robust Kalman filter for relative navigation using global position system","volume":"7","author":"Li","year":"2013","journal-title":"Radar Sonar Navig. IET"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Song, K., Cong, S., Deng, K., Shang, W., Kong, D., and Shen, H. (2014, January 28\u201330). Design of adaptive strong tracking and robust Kalman filter. Proceedings of the 33rd Chinese Control Conference, Nanjing, China.","DOI":"10.1109\/ChiCC.2014.6896087"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4462","DOI":"10.1109\/TVT.2011.2168249","article-title":"A DSRC Doppler-Based Cooperative Positioning Enhancement for Vehicular Networks with GPS Availability","volume":"60","author":"Alam","year":"2011","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3770","DOI":"10.1109\/TSP.2012.2194705","article-title":"Improved Position Estimation Using Hybrid TW-TOA and TDOA in Cooperative Networks","volume":"60","author":"Gholami","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1186\/1687-6180-2013-150","article-title":"Robust all-source positioning of UAVs based on belief propagation","volume":"2013","author":"Chen","year":"2013","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-015-0493-x","article-title":"Space-borne BDS receiver for LING QIAO satellite: Design, implementation and preliminary in-orbit experiment results","volume":"20","author":"Chen","year":"2016","journal-title":"GPS Solut."},{"key":"ref_22","unstructured":"Unwin, M., De Vos Van Steenwijk, R., and Gommenginger, C. (2010, January 21\u201324). The SGR-ReSI\u2014A new generation of space GNSS receiver for remote sensing. Proceedings of the 23rd International Technical Meeting of the Satellite Division of the Institute of Navigation ION GNSS, Portland, OR, USA."},{"key":"ref_23","unstructured":"Huber, P.J., and Ronchetti, E.M. (2011). Robust Statistics, John Wiley & Sons Inc.. [2nd ed.]."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1109\/JPROC.2012.2190154","article-title":"Satellite Navigation for Aviation in 2025","volume":"100","author":"Blanch","year":"2012","journal-title":"Proc. IEEE"},{"key":"ref_25","first-page":"271","article-title":"Robust Kalman-type Filtering in Positioning Applications","volume":"Volume 14","author":"Kordic","year":"2010","journal-title":"Kalman Filter"},{"key":"ref_26","first-page":"138","article-title":"Revisiting the doppler filter of LEO satellite GNSS receivers for precise velocity estimation","volume":"30","author":"Chen","year":"2013","journal-title":"J. Electron."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1109\/TAES.2012.6129674","article-title":"Improving the Design of Frequency Lock Loops for GNSS Receivers","volume":"48","author":"Curran","year":"2012","journal-title":"IEEE Trans. Aerospace Electron. Syst."},{"key":"ref_28","first-page":"56","article-title":"Statistical Orbit Determination","volume":"48","author":"Schutz","year":"2004","journal-title":"Am. Press"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Leschziner, M. (2015). Statistical Turbulence Modelling for Fluid Dynamics, Imperial College Press.","DOI":"10.1142\/p997"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2327\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:21:28Z","timestamp":1760361688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2327"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,19]]},"references-count":29,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20082327"],"URL":"https:\/\/doi.org\/10.3390\/s20082327","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,4,19]]}}}