{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T15:37:57Z","timestamp":1781624277299,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T00:00:00Z","timestamp":1652745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research Program of China Collaborative Precision Positioning Project","award":["2016YFB0501900"],"award-info":[{"award-number":["2016YFB0501900"]}]},{"name":"National Key Research Program of China Collaborative Precision Positioning Project","award":["41774017"],"award-info":[{"award-number":["41774017"]}]},{"name":"National Key Research Program of China Collaborative Precision Positioning Project","award":["41974008"],"award-info":[{"award-number":["41974008"]}]},{"name":"National Natural Science Foundation of China","award":["2016YFB0501900"],"award-info":[{"award-number":["2016YFB0501900"]}]},{"name":"National Natural Science Foundation of China","award":["41774017"],"award-info":[{"award-number":["41774017"]}]},{"name":"National Natural Science Foundation of China","award":["41974008"],"award-info":[{"award-number":["41974008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Satellite clock offset is an important factor affecting the accuracy of real-time precise point positioning (RT-PPP). Due to missing real-time service (RTS) products provided by the International GNSS Service (IGS) or network faults, users may not obtain effective real-time corrections, resulting in the unavailability of RT-PPP. Considering this issue, an improved back propagation (BP) neural network optimized by heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer (HPSO-BP) is proposed for clock offset prediction. The new model uses the particle swarm optimizer to optimize the initial parameters of the BP neural network, which can avoid the instability and over-fitting problems of the traditional BP neural network. IGS RTS product data is selected for the experimental analysis; the results demonstrate that the average prediction precision of the HPSO-BP model for 20-min and 60-min is better than 0.15 ns, improving by approximately 85% compared to traditional models including the linear polynomial (LP) model, the quadratic polynomial (QP) model, the gray system model (GM (1,1)), and the ARMA time series model. It indicates that the HPSO-BP model has reasonable practicability and stability in the short-term satellite clock offset prediction, and its prediction performance is superior to traditional models. Therefore, in practical applications, the clock offset products predicted by the HPSO-BP model can meet the centimeter-level positioning accuracy requirements of RT-PPP.<\/jats:p>","DOI":"10.3390\/rs14102407","type":"journal-article","created":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T03:20:43Z","timestamp":1652844043000},"page":"2407","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Prediction of GPS Satellite Clock Offset Based on an Improved Particle Swarm Algorithm Optimized BP Neural Network"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8023-0820","authenticated-orcid":false,"given":"Dong","family":"Lv","sequence":"first","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Genyou","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jikun","family":"Ou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6095-287X","authenticated-orcid":false,"given":"Shengliang","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Gao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1029\/GL017i005p00651","article-title":"Geodetic point positioning with GPS carrier beat phase data from the CASA UNO Experiment","volume":"17","author":"Malys","year":"2013","journal-title":"Geophys. Res. Lett."},{"key":"ref_2","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. Solid Earth"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1007\/s10291-016-0583-4","article-title":"Maintaining real-time precise point positioning during outages of orbit and clock corrections","volume":"21","author":"Deo","year":"2017","journal-title":"GPS Solut."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jiao, G., and Song, S. (2022). High-Rate One-Hourly Updated Ultra-Rapid Multi-GNSS Satellite Clock Offsets Estimation and Its Application in Real-Time Precise Point Positioning. Remote Sens., 14.","DOI":"10.3390\/rs14051257"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s10291-015-0467-z","article-title":"Performance of real-time Precise Point Positioning using IGS real-time service","volume":"20","author":"Elsobeiey","year":"2016","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/s10291-019-0856-9","article-title":"Investigation of the performance of real-time BDS-only precise point positioning using the IGS real-time service","volume":"23","author":"Wang","year":"2019","journal-title":"GPS Solut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s10291-014-0369-5","article-title":"IGS RTS precise orbits and clocks verification and quality degradation over time","volume":"19","author":"Hadas","year":"2015","journal-title":"GPS Solut."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s10291-017-0681-y","article-title":"An approach to GPS clock prediction for real-time PPP during outages of RTS stream","volume":"22","author":"Nie","year":"2017","journal-title":"GPS Solut."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10291-019-0859-6","article-title":"A new datum jump detection and mitigation method of Real-Time Service (RTS) clock products","volume":"23","author":"Zhang","year":"2019","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1088\/1681-7575\/aa6f62","article-title":"Atomic clock prediction algorithm: Random pursuit strategy","volume":"54","author":"Wang","year":"2017","journal-title":"Metrologia"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1017\/S0373463317001035","article-title":"Fusion-based Satellite Clock Bias Prediction Considering Characteristics and Fitted Residue","volume":"71","author":"Lu","year":"2018","journal-title":"J. Navig."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2889","DOI":"10.1016\/j.asr.2018.01.020","article-title":"Atomic clock performance and combined clock error prediction for the new generation of BeiDou navigation satellites","volume":"63","author":"Wang","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_13","first-page":"132","article-title":"The Prediction of BeiDou Satellite Clock Bias Based on Periodic Term and Starting Point Deviation Correction","volume":"45","author":"Ai","year":"2016","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_14","first-page":"83","article-title":"Real-Time Clock Offset Prediction Model with Periodic and Neural Network Corrections","volume":"39","author":"Huang","year":"2018","journal-title":"J. Astronaut."},{"key":"ref_15","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_16","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":"Hauschild","year":"2013","journal-title":"GPS Solut."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1016\/j.asr.2012.09.041","article-title":"Quality variation of GPS satellite clocks on-orbit using IGS clock products","volume":"51","author":"Huang","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1038\/s41467-019-09186-x","article-title":"Network-based prediction of drug combinations","volume":"10","author":"Cheng","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1007\/s10291-021-01115-0","article-title":"Clock bias prediction algorithm for navigation satellites based on a supervised learning long short-term memory neural network","volume":"25","author":"Huang","year":"2021","journal-title":"GPS Solut."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ai, Q.S., Xu, T.H., Li, J.J., and Xiong, H.W. (2016, January 18\u201320). The Short-Term Forecast of BeiDou Satellite Clock Bias Based on Wavelet Neural Network. Proceedings of the 7th China Satellite Navigation Conference (CSNC), Changsha, China.","DOI":"10.1007\/978-981-10-0934-1_14"},{"key":"ref_21","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_22","first-page":"39","article-title":"Satellites clock bias forecast based on gray system and BP neural network","volume":"26","author":"Han","year":"2012","journal-title":"J. Shandong Univ. Technol. (Nat. Sci. Ed.)"},{"key":"ref_23","first-page":"993","article-title":"Prediction of the satellite clock bias based on MEA-BP neural network","volume":"49","author":"Lv","year":"2020","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhao, W., Liu, G., Wang, S., Gao, M., and Lv, D. (2021). Real-Time Estimation of GPS-BDS Inter-System Biases: An Improved Particle Swarm Optimization Algorithm. Remote Sens., 13.","DOI":"10.3390\/rs13163214"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1016\/j.ijepes.2014.09.005","article-title":"Particle swarm optimization with an aging leader and challengers algorithm for optimal power flow problem with FACTS devices","volume":"64","author":"Singh","year":"2015","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.ins.2020.06.027","article-title":"Heterogeneous comprehensive learning and dynamic multi- swarm particle swarm optimizer with two mutation operators","volume":"540","author":"Wang","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_27","first-page":"323","article-title":"Research the algorithm of wavelet neural network to predict satellite clock bias","volume":"42","author":"Wang","year":"2013","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_28","first-page":"373","article-title":"A new data preprocessing method for satellite clock bias and its application in WNN to predict medium-term and long-term clock bias","volume":"41","author":"Wang","year":"2016","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s10291-020-01019-5","article-title":"A high-precision short-term prediction method with stable performance for satellite clock bias","volume":"24","author":"Wang","year":"2020","journal-title":"GPS Solut."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2015.07.035","article-title":"Dynamic mentoring and self-regulation based particle swarm optimization algorithm for solving complex real-world optimization problems","volume":"326","author":"Tanweer","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_31","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":"2017","journal-title":"GPS Solut."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/10\/2407\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:13:45Z","timestamp":1760138025000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/10\/2407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,17]]},"references-count":31,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["rs14102407"],"URL":"https:\/\/doi.org\/10.3390\/rs14102407","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,17]]}}}