{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T17:07:49Z","timestamp":1763226469845,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,6,6]],"date-time":"2017-06-06T00:00:00Z","timestamp":1496707200000},"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>The application of real-time precise point positioning (PPP) requires real-time precise orbit and clock products that should be predicted within a short time to compensate for the communication delay or data gap. Unlike orbit correction, clock correction is difficult to model and predict. The widely used linear model hardly fits long periodic trends with a small data set and exhibits significant accuracy degradation in real-time prediction when a large data set is used. This study proposes a new prediction model for maintaining short-term satellite clocks to meet the high-precision requirements of real-time clocks and provide clock extrapolation without interrupting the real-time data stream. Fast Fourier transform (FFT) is used to analyze the linear prediction residuals of real-time clocks. The periodic terms obtained through FFT are adopted in the sliding window prediction to achieve a significant improvement in short-term prediction accuracy. This study also analyzes and compares the accuracy of short-term forecasts (less than 3 h) by using different length observations. Experimental results obtained from International GNSS Service (IGS) final products and our own real-time clocks show that the 3-h prediction accuracy is better than 0.85 ns. The new model can replace IGS ultra-rapid products in the application of real-time PPP. It is also found that there is a positive correlation between the prediction accuracy and the short-term stability of on-board clocks. Compared with the accuracy of the traditional linear model, the accuracy of the static PPP using the new model of the 2-h prediction clock in N, E, and U directions is improved by about 50%. Furthermore, the static PPP accuracy of 2-h clock products is better than 0.1 m. When an interruption occurs in the real-time model, the accuracy of the kinematic PPP solution using 1-h clock prediction product is better than 0.2 m, without significant accuracy degradation. This model is of practical significance because it solves the problems of interruption and delay in data broadcast in real-time clock estimation and can meet the requirements of real-time PPP.<\/jats:p>","DOI":"10.3390\/s17061308","type":"journal-article","created":{"date-parts":[[2017,6,6]],"date-time":"2017-06-06T10:53:09Z","timestamp":1496746389000},"page":"1308","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Improved Short-Term Clock Prediction Method for Real-Time Positioning"],"prefix":"10.3390","volume":"17","author":[{"given":"Yifei","family":"Lv","sequence":"first","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiqiang","family":"Dai","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qile","family":"Zhao","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sheng","family":"Yang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinning","family":"Zhou","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingnan","family":"Liu","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5005","DOI":"10.1029\/96JB03860","article-title":"Precise point positioning for the efficient and robust analysis of GPS data from large networks","volume":"102","author":"Zumberge","year":"1997","journal-title":"J. Geophys. Res."},{"key":"ref_2","unstructured":"Kouba, J. (2009). A Guide to Using International GNSS Service (IGS) Products."},{"key":"ref_3","unstructured":"(2016, August 17). International GNSS Service Products. Available online: http:\/\/www.igs.org\/products."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/s11806-010-0226-9","article-title":"Impact of sampling rate of IGS satellite clock on precise point positioning","volume":"13","author":"Guo","year":"2010","journal-title":"Geo-spat. Inf. Sci."},{"key":"ref_5","unstructured":"(2016, August 17). IGS Real-Time Service Fact Sheet. Available online: http:\/\/kb.igs.org\/hc\/en-us\/articles\/201087803-IGS-Real-Time-Service-Fact-Sheet."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s10291-012-0278-4","article-title":"Short-term analysis of GNSS clocks","volume":"17","author":"Steigenberger","year":"2013","journal-title":"GPS Solut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1002\/2015RS005667","article-title":"Short-term GNSS satellite clock stability","volume":"50","author":"Griggs","year":"2015","journal-title":"Radio Sci."},{"key":"ref_8","first-page":"118","article-title":"Research on estimation and precision of GPS satellite clock error","volume":"29","author":"Huang","year":"2009","journal-title":"J. Geod. Geodyn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s10291-008-0089-9","article-title":"Characterization of periodic variations in the GPS satellite clocks","volume":"12","author":"Senior","year":"2008","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/s10291-016-0543-z","article-title":"Improving prediction performance of GPS satellite clock bias based on wavelet neural network","volume":"21","author":"Wang","year":"2016","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zheng, Z., Lu, X., and Chen, Y. (2008, January 18\u201320). Improved Grey Model and Application in Real-Time GPS Satellite Clock Bias Prediction (419\u2013423). Proceedings of the IEEE 2008 Fourth International Conference on Natural Computation, Jinan, China.","DOI":"10.1109\/ICNC.2008.630"},{"key":"ref_12","unstructured":"Sun, J., Liu, J., Fan, S., and Wang, F. (2016). Characteristic analysis and short-term prediction of GPS\/BDS satellite clock correction. Lecture Notes in Electrical Engineering, Proceedings of the China Satellite Navigation Conference (CSNC), Changsha, China, 18\u201320 May 2016, Springer."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s10291-013-0313-0","article-title":"Real-time clock correction prediction with an improved model","volume":"18","author":"Huang","year":"2013","journal-title":"GPS Solut."},{"key":"ref_14","unstructured":"Lou, Y.D. (2008). Research on Real-Time Precise GPS Orbit and Clock Correction Determination, Wuhan University."},{"key":"ref_15","unstructured":"Song, W.W. (2011). Research on Real-Time Clock Correction Determination and Real-time Precise Point Positioning, Wuhan University."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ahmed, N., and Rao, K.R. (1975). Fast Fourier Transform[M] Orthogonal Transforms for Digital Signal Processing, Springer.","DOI":"10.1007\/978-3-642-45450-9"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Riley, W.J. (2007). Handbook of Frequency Stability Analysis.","DOI":"10.6028\/NIST.SP.1065"},{"key":"ref_18","unstructured":"US Air Force (2006). NAVSTAR GPS Space Segment\/Navigation User Interfaces."},{"key":"ref_19","unstructured":"Senior, K., Koppang, P., and Matsakis, D. (2011, January 8). Developing an IGS time scale. Proceedings of the 2001 IEEE International Frequncy Control Symposium and PDA Exhibition (Cat. No. 01CH37218), Seattle, WA, USA."},{"key":"ref_20","unstructured":"(2016, August 17). Figures and Statistics for Precise Point Positioning (PPP). Available online: http:\/\/www-app2.gfz-potsdam.de\/pb1\/igsacc\/index_igsacc_ppp.html."},{"key":"ref_21","unstructured":"(2016, August 17). The Crustal Dynamics Data Information System (CDDIS) Data and Derived Products, Available online: ftp:\/\/cddis.gsfc.nasa.gov\/pub\/gps."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/PL00012863","article-title":"New IGS Station and Satellite Clock Combination","volume":"4","author":"Kouba","year":"2001","journal-title":"GPS Solut."},{"key":"ref_23","unstructured":"Zhao, Q.L., Dai, Z.Q., Wang, G.X., Li, X.T., and Liu, J.N. (2016). Real-Time Precise BDS Clock Estimation with the Undifferenced Observation, Geomatics and Information Science of Wuhan University."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s00190-007-0208-3","article-title":"Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations","volume":"82","author":"Ge","year":"2008","journal-title":"J. Geod."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/6\/1308\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:38:10Z","timestamp":1760207890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/6\/1308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,6]]},"references-count":24,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2017,6]]}},"alternative-id":["s17061308"],"URL":"https:\/\/doi.org\/10.3390\/s17061308","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,6,6]]}}}