{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T07:14:51Z","timestamp":1766733291720,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,11]],"date-time":"2021-01-11T00:00:00Z","timestamp":1610323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Satellite timing is an effective and convenient method that has been widely accepted in the time community. The key to satellite timing is obtaining a clean receiver clock offset. In this paper, instead of regarding the receiver clock offset as white noise, a two-state stochastic clock model involving three kinds of noise was conceived and used in PPP filter estimation. The influence of clock type and sampling time on satellite timing performance was first analysed. In addition, the kinematic scheme and static scheme were both investigated for meeting the demands of multi-occasional users. The values show that the model works well for both the kinematic scheme and static scheme; in contrast to that of the white noise model, the timing stability is enhanced at all the sampling times. For the six stations, especially when the averaging time is less than 1000 s, the average stability improvement values of the kinematic scheme are 75.53, 43.24, 75.00, 69.05, 40.57, and 25.45%, and the average improvement values of the static scheme are 65.49, 77.94, 56.71, 60.78, 64.41, and 39.41%. Furthermore, the enhancement magnitude is related to clock type. For a high-stability clock, the improvement of the kinematic scheme is greater than that of the static scheme, whereas for a low-stability clock, the improvement of the kinematic scheme is less than that of the static scheme.<\/jats:p>","DOI":"10.3390\/s21020466","type":"journal-article","created":{"date-parts":[[2021,1,11]],"date-time":"2021-01-11T11:36:11Z","timestamp":1610364971000},"page":"466","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Benefits of Receiver Clock Modelling in Satellite Timing"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2883-9281","authenticated-orcid":false,"given":"Weijin","family":"Qin","sequence":"first","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"}]},{"given":"Xiao","family":"Wang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"}]},{"given":"Hang","family":"Su","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"}]},{"given":"Zhe","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"}]},{"given":"Xiao","family":"Li","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"}]},{"given":"Xuhai","family":"Yang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s10291-013-0321-0","article-title":"Quantitative evaluation of multipath rejection capabilities of GNSS antennas","volume":"18","author":"Boccia","year":"2013","journal-title":"GPS Solut."},{"key":"ref_2","unstructured":"Leute, J. (2018). Characterization and evaluation of GPS PPP techniques for optical clock comparisons. [Ph.D. Thesis, Leibniz Universit\u00e4t Hannover]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s10291-014-0377-5","article-title":"Monitoring of UTC(k)\u2019s using PPP and IGS real-time products","volume":"19","author":"Defraigne","year":"2014","journal-title":"GPS Solut."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1088\/0026-1394\/52\/2\/301","article-title":"Perosanz, 1 \u00d7 10\u221216 frequency transfer by GPS PPP with integer ambiguity resolution","volume":"52","author":"Petit","year":"2015","journal-title":"Metrologia"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1088\/1681-7575\/aaa673","article-title":"Progress of BeiDou time transfer at NTSC","volume":"55","author":"Guang","year":"2018","journal-title":"Metrologia"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1017\/S0373463318000486","article-title":"Improving Galileo\u2019s Carrier-Phase Time Transfer Based on Prior Constraint Information","volume":"72","author":"Zhang","year":"2018","journal-title":"J. Navig."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Tu, R., Zhang, P., Zhang, R., Liu, J., and Lu, X. (2018). Modeling and Assessment of Precise Time Transfer by Using BeiDou Navigation Satellite System Triple-Frequency Signals. Sensors, 18.","DOI":"10.3390\/s18041017"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s00190-018-1178-3","article-title":"Multi-GNSS satellite clock estimation constrained with oscillator noise model in the existence of data discontinuity","volume":"93","author":"Shi","year":"2018","journal-title":"J. Geod."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4401","DOI":"10.1002\/2016JD026184","article-title":"A directional model of tropospheric horizontal gradients in Global Positioning System and its application for particular weather scenarios","volume":"122","author":"Masoumi","year":"2017","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1007\/s10291-015-0480-2","article-title":"Benefits of receiver clock modeling in code-based GNSS navigation","volume":"20","author":"Krawinkel","year":"2015","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s00190-013-0616-5","article-title":"Stochastic modeling of high-stability ground clocks in GPS analysis","volume":"87","author":"Wang","year":"2013","journal-title":"J. Geod."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s10291-018-0814-y","article-title":"Enhancing real-time precise point positioning time and frequency transfer with receiver clock modeling","volume":"23","author":"Ge","year":"2018","journal-title":"GPS Solut."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ge, Y., Dai, P., Qin, W., Yang, X., Zhou, F., Wang, S., and Zhao, X. (2019). Performance of Multi-GNSS Precise Point Positioning Time and Frequency Transfer with Clock Modeling. Remote Sens., 11.","DOI":"10.3390\/rs11030347"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1016\/j.asr.2019.10.029","article-title":"Real-time clock comparison and monitoring with multi-GNSS precise point positioning: GPS, GLONASS and Galileo","volume":"65","author":"Lyu","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"04018003","DOI":"10.1061\/(ASCE)SU.1943-5428.0000252","article-title":"Satellite-Clock Modeling in Single-Frequency PPP-RTK Processing","volume":"144","author":"Wang","year":"2018","journal-title":"J. Surv. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3773","DOI":"10.1002\/2015GL063632","article-title":"Improved GPS-based coseismic displacement monitoring using high-precision oscillators","volume":"42","author":"Weinbach","year":"2015","journal-title":"Geophys. Res. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1088\/0026-1394\/50\/6\/586","article-title":"An adaptive oscillator noise analysis using factor analysis","volume":"50","author":"Cheng","year":"2013","journal-title":"Metrologia"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Huang, G., Cui, B., Zhang, Q., Fu, W., and Li, P. (2018). An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets. Remote Sens., 10.","DOI":"10.3390\/rs10010060"},{"key":"ref_19","unstructured":"Koch, D., and Rothacher, M. (2018, January 4\u201313). Satellite clock modeling for kinematic determination. Proceedings of the 20th EGU General Assembly, EGU 2018 Conference, Vienna, Austria."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s10291-012-0297-1","article-title":"Improved GRACE kinematic orbit determination using GPS receiver clock modeling","volume":"17","author":"Weinbach","year":"2012","journal-title":"GPS Solut."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Allan, D.W., and Barnes, J.A. (1981, January 27\u201329). A modified \u201cAllan variance\u201d with increased oscillator characterization ability. Proceedings of the Thirty Fifth Annual Frequency Control Symposium 1981, Philadelphia, PA, USA.","DOI":"10.1109\/FREQ.1981.200514"},{"key":"ref_22","unstructured":"Petit, G., and Luzum, B. IERS Conventions (2010). Bureau International des Poids et Mesures Sevres (France). (2010) (No. IERS-TN-36)."},{"key":"ref_23","first-page":"91","article-title":"Effects of antenna orienation on GPS carrier phase","volume":"18","author":"Wu","year":"1992","journal-title":"Manuscr. Geod."},{"key":"ref_24","first-page":"1","article-title":"Alternative Strategy for Estimating Zenith Tropospheric Delay from Precise Point Positioning","volume":"100","author":"Mohammed","year":"2017","journal-title":"Atmos. Meas. Tech. Discuss."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Petit, G., Leute, J., Loyer, S., and Perosanz, F. (2017, January 9\u201313). Sub 10\u201316 frequency transfer with IPPP: Recent results. Proceedings of the 2017 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF\/IFCS), Besancon, France.","DOI":"10.1109\/FCS.2017.8089035"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4025","DOI":"10.1029\/2017JB015060","article-title":"GPS\/GLONASS Combined Precise Point Positioning with the Modeling of Highly-stable Receiver Clock in the Application of Monitoring Active Seismic Deformation","volume":"123","author":"Chen","year":"2018","journal-title":"J. Geophys. Res. Solid Earth"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/466\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:09:49Z","timestamp":1760159389000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/466"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,11]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21020466"],"URL":"https:\/\/doi.org\/10.3390\/s21020466","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,1,11]]}}}