{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T10:25:35Z","timestamp":1775039135652,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,1,25]],"date-time":"2019-01-25T00:00:00Z","timestamp":1548374400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Fund of China","award":["41874031"],"award-info":[{"award-number":["41874031"]}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["cstc2016jcyjA0300"],"award-info":[{"award-number":["cstc2016jcyjA0300"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["cstc2018jcyjAX0127"],"award-info":[{"award-number":["cstc2018jcyjAX0127"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["cstc2016jcyjA0378"],"award-info":[{"award-number":["cstc2016jcyjA0378"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Technology Innovation Program of Hubei Province","award":["2018AAA070"],"award-info":[{"award-number":["2018AAA070"]}]},{"name":"Natural Science Fund of Hubei Province","award":["2018CFA007"],"award-info":[{"award-number":["2018CFA007"]}]},{"name":"Major Research Plan of the National Natural Science Foundation of China","award":["11632004"],"award-info":[{"award-number":["11632004"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2018CDXYHK0016"],"award-info":[{"award-number":["2018CDXYHK0016"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Cycle slip (CS) is a primary error source in Precise Point Positioning\/Inertial Navigation System (PPP\/INS) integrated systems. In this study, an INS-aided CS detection and repair method is presented. It utilizes high-precision INS information instead of a pseudorange to remove the satellite\u2013receiver geometric range in the wide-lane (WL) and ionospheric-free (IF) phase combinations and creates an INS-aided WL (WL-INS) model and an INS-aided IF (IF-INS) model. Since INS information is superior to pseudorange, the INS-aided models have high detection accuracy. However, the effectiveness of INS-aided models cannot persist for a long time because of INS accumulation error. To overcome the disturbance of INS error, improved INS-aided models are proposed. This idea takes advantage of the long wavelength of WL combination and tries to fix WL CS. Once it succeeds, the INS error can be evaluated and removed. The proposed method was tested using land vehicle data, in which simulated cycle slips and signal interruption were introduced. The results show that this method can accurately detect and repair different cycle slips between the continuous Global Positioning System (GPS) epoch. When it comes to the cycle slip after a GPS interruption, the method can also accelerate PPP re-convergence, as it is not affected by the inertial accumulation error.<\/jats:p>","DOI":"10.3390\/s19030502","type":"journal-article","created":{"date-parts":[[2019,1,25]],"date-time":"2019-01-25T11:30:00Z","timestamp":1548415800000},"page":"502","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Effective Cycle Slip Detection and Repair for PPP\/INS Integrated Systems"],"prefix":"10.3390","volume":"19","author":[{"given":"Sheng","family":"Yang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6972-4344","authenticated-orcid":false,"given":"Leilei","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Optoelectronic Technology and Systems of the Ministry of Education of China, Chongqing University, Chongqing 400044, China"},{"name":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingbin","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China"},{"name":"Department of Remote Sensing and Photogrammetry and the Center of Excellence in Laser Scanning Research, Finnish Geospatial Research Institute, Masala 02430, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0068-0141","authenticated-orcid":false,"given":"Qusen","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuewen","family":"Ding","sequence":"additional","affiliation":[{"name":"Qianxun Spatial Intelligence Inc, Shanghai 200438, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongxing","family":"Sun","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9319-9498","authenticated-orcid":false,"given":"Yu","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunhua","family":"Ren","sequence":"additional","affiliation":[{"name":"Key Laboratory of Optoelectronic Technology and Systems of the Ministry of Education of China, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6444-8467","authenticated-orcid":false,"given":"Ning","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,25]]},"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. Solid Earth"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1002\/j.2161-4296.2002.tb00265.x","article-title":"High-precision, kinematic positioning with a single GPS receiver","volume":"49","author":"Bisnath","year":"2002","journal-title":"Navigation"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"14344","DOI":"10.3390\/s121114344","article-title":"Inertial aided cycle slip detection and identification for integrated PPP GPS and INS","volume":"12","author":"Du","year":"2012","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s10291-015-0452-6","article-title":"A double-differenced cycle slip detection and repair method for GNSS CORS network","volume":"20","author":"Chen","year":"2016","journal-title":"GPS Solut."},{"key":"ref_5","unstructured":"Bisnath, S.B., and Langley, R.B. (May, January 30). Automated cycle-slip correction of dual-frequency kinematic GPS data. Proceedings of the 47th Annual Conference of the Canadian Aeronautics and Space Institute, Ottawa, ON, Canada."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s10291-011-0237-5","article-title":"Real-time cycle slip detection in triple-frequency GNSS","volume":"16","author":"Lacy","year":"2012","journal-title":"GPS Solut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s10291-014-0396-2","article-title":"Real-time detection and repair of cycle slips in triple-frequency GNSS measurements","volume":"19","author":"Zhao","year":"2015","journal-title":"GPS Solut."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1029\/GL017i003p00199","article-title":"An automatic editing algorithm for GPS data","volume":"17","author":"Blewitt","year":"1990","journal-title":"Geophys. Res. Lett."},{"key":"ref_9","unstructured":"Lichten, S.M., Bar-Sever, Y.E., Bertiger, E.I., Heflin, M., Hurst, K., Muellerschoen, R.J., Wu, S.C., Yunck, T.P., and Zumberge, J.F. (1995, January 24\u201326). GIPSY-OASIS II: A high precision GPS data processing system and general orbit analysis tool, technology 2006. Proceedings of the NASA Technology Transfer Conference, Chicago, IL, USA."},{"key":"ref_10","unstructured":"Beutler, G., Bock, H., Brockman, E., and Dach, R. (2001). Bernese GPS Software, Astronomical Institute of Bern. version 4.2."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1007\/BF02899825","article-title":"PANDA software and its preliminary result of positioning and orbit determination","volume":"8","author":"Liu","year":"2003","journal-title":"Wuhan Univ. J. Nat. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s00190-010-0426-y","article-title":"A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver","volume":"85","author":"Liu","year":"2011","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10291-012-0275-7","article-title":"Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity","volume":"17","author":"Cai","year":"2013","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s00190-007-0203-8","article-title":"The Bayesian detection of discontinuities in a polynomial regression and its application to the cycle slip problem","volume":"82","author":"Reguzzoni","year":"2008","journal-title":"J. Geod."},{"key":"ref_15","unstructured":"Banville, S., and Langley, R.B. (2009, January 22\u201325). Improving real-time kinematic PPP with instantaneous cycle-slip correction. Proceedings of the ION GNSS 2009, Institute of Navigation, Savannah, GA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s00190-010-0404-4","article-title":"Rapid re-convergences to ambiguity-fixed solutions in precise point positioning","volume":"84","author":"Geng","year":"2010","journal-title":"J. Geod."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"25336","DOI":"10.3390\/s151025336","article-title":"GPS cycle slip detection considering satellite geometry based on TDCP\/INS integrated navigation","volume":"15","author":"Kim","year":"2015","journal-title":"Sensors"},{"key":"ref_18","unstructured":"Colombo, O.L., Bhapkar, U.V., and Evans, A.G. (1999, January 14\u201317). Inertial-aided cycle-slip detection\/correction for precise, long-baseline kinematic GPS. Proceedings of the ION GPS, Nashville, TN, USA."},{"key":"ref_19","unstructured":"Altmayer, C. (2000, January 3\u20135). Enhancing the integrity of integrated GPS\/INS systems by cycle slip detection and correction. Proceedings of the IEEE Intelligent Vehicles Symposium, Dearborn, MI, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1017\/S0373463303002443","article-title":"Effective cycle slip detection and identification for high precision GPS\/INS integrated systems","volume":"56","author":"Lee","year":"2003","journal-title":"J. Navig."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"15261","DOI":"10.1029\/1998JB900067","article-title":"Modeling weather fronts to improve GPS heights: A new tool for GPS meteorology","volume":"104","author":"Gregorius","year":"1999","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1029\/2007GL030889","article-title":"Kinematic GPS solutions for aircraft trajectories: identifying and minimizing systematic height errors associated with atmospheric propagation delays","volume":"34","author":"Shan","year":"2007","journal-title":"Geophys. Res. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4514","DOI":"10.3390\/s130404514","article-title":"Estimating zenith tropospheric delays from beidou navigation satellite system observations","volume":"13","author":"Xu","year":"2013","journal-title":"Sensors"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1007\/s00190-002-0286-1","article-title":"Predicting atmospheric biases for real-time ambiguity resolution in GPS\/GLONASS reference station networks","volume":"76","author":"Dai","year":"2003","journal-title":"J. Geod."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10291-010-0174-8","article-title":"Spherical cap harmonic model for mapping and predicting regional TEC","volume":"15","author":"Liu","year":"2011","journal-title":"GPS Solut."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1016\/j.asr.2012.03.016","article-title":"An improved approach to model ionospheric delays for single-frequency precise point positioning","volume":"49","author":"Shi","year":"2012","journal-title":"Adv. Space Res."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Nykiel, G., Zanimonskiy, Y., Yampolski, Y., and Figurski, M. (2017). Efficient Usage of Dense GNSS Networks in Central Europe for the Visualization and Investigation of Ionospheric TEC Variations. Sensors, 17.","DOI":"10.3390\/s17102298"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s10291-011-0233-9","article-title":"Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing","volume":"16","author":"Zhang","year":"2012","journal-title":"GPS Solut."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/502\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:28:40Z","timestamp":1760185720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/502"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,25]]},"references-count":28,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["s19030502"],"URL":"https:\/\/doi.org\/10.3390\/s19030502","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,25]]}}}