{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:42:02Z","timestamp":1760233322479,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T00:00:00Z","timestamp":1672358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFB3901301","42274022"],"award-info":[{"award-number":["2021YFB3901301","42274022"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["2021YFB3901301","42274022"],"award-info":[{"award-number":["2021YFB3901301","42274022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Since 23 June 2020, BDS-3 has been entirely operated and obtained the ability of global PNT (Positioning, Navigation, and Timing) services. Afterward, real-time Precise Point Positioning (PPP) service is available in China\u2019s surrounding areas via BDS-3 PPP-B2b signal. However, such a real-time PPP service cannot maintain the high accuracy and continuity of positioning solutions in challenging environments, such as urban environments. For that, we carried out a model by integrating between-satellite single-differenced (BSSD) PPP, a low-cost Inertial Navigation System (INS), and an odometer via an extended Kalman filter. The performance of this integration model was assessed with vehicle-borne data. Results demonstrated that (1) the position RMS (Root Mean Square) of BSSD PPP are 64.33 cm, 53.47 cm, and 154.11 cm. Compared with BSSD PPP, about 31.2%, 23.3%, and 27.3% position improvements can be achieved by using INS. Further enhancements of position RMS benefiting from the odometer are 1.34%, 1.41%, and 1.73% in the three directions. (2) Anyway, the accuracy of BSSD PPP\/INS\/Odometer tightly coupled integration is slightly higher than that of undifferenced PPP\/INS\/Odometer integration, with average improvement percentages of 7.71%, 3.09%, and 0.27%. Meanwhile, the performance of BSSD PPP\/INS\/Odometer integration during the periods with satellite outages is better than the undifferenced PPP-based solutions. (3) The improvements in attitudes from an odometer are more significant on heading angle than the other two attitudes, with percentages of 25.00%. (4) During frequent GNSS outage periods, the reduction in average maximum position drifts provided by INS are 18.01%, 8.95%, and 20.74%. After integrating with an odometer, the drifts can be furtherly decreased by 25.11%, 15.96%, and 20.69%. For attitude, about 41.67% reduction in average maximum drifts of heading angles is obtained.<\/jats:p>","DOI":"10.3390\/rs15010199","type":"journal-article","created":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T03:19:46Z","timestamp":1672370386000},"page":"199","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Low-Cost IMU and Odometer Tightly Augmented PPP-B2b-Based Inter-Satellite Differenced PPP in Urban Environments"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7883-7455","authenticated-orcid":false,"given":"Yu","family":"Min","sequence":"first","affiliation":[{"name":"School of Land Science and Technology, China University of Geosciences Beijing, Beijing 100083, China"},{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7997-7719","authenticated-orcid":false,"given":"Zhouzheng","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Land Science and Technology, China University of Geosciences Beijing, Beijing 100083, China"}]},{"given":"Jie","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Land Science and Technology, China University of Geosciences Beijing, Beijing 100083, China"}]},{"given":"Ruohua","family":"Lan","sequence":"additional","affiliation":[{"name":"School of Land Science and Technology, China University of Geosciences Beijing, Beijing 100083, China"}]},{"given":"Qiaozhuang","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Land Science and Technology, China University of Geosciences Beijing, Beijing 100083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8851-0261","authenticated-orcid":false,"given":"Cheng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Land Science and Technology, China University of Geosciences Beijing, Beijing 100083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1007\/s11430-017-9186-9","article-title":"Progress and Performance Evaluation of BeiDou Global Navigation Satellite System: Data Analysis Based on BDS-3 Demonstration System","volume":"61","author":"Yang","year":"2018","journal-title":"Sci. China Earth Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1007\/s11430-013-4769-0","article-title":"Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system","volume":"57","author":"Yang","year":"2014","journal-title":"Sci. China Earth Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Teunissen, M. (2017). Chinese navigation satellite systems. Handbook of Global Navigation Satellite Systems, Springer. Chapter 10.","DOI":"10.1007\/978-3-319-42928-1"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"110453","DOI":"10.1016\/j.measurement.2021.110453","article-title":"Modeling and Assessment of Multi-Frequency GPS\/BDS-2\/BDS-3 Kinematic Precise Point Positioning Based on Vehicle-Borne Data","volume":"189","author":"Lv","year":"2022","journal-title":"Measurement"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"109355","DOI":"10.1016\/j.measurement.2021.109355","article-title":"Modeling of BDS-2\/BDS-3 Single-Frequency PPP with B1I and B1C Signals and Positioning Performance Analysis","volume":"178","author":"Shi","year":"2021","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"25001","DOI":"10.1088\/1361-6501\/ab41cf","article-title":"Improving BDS-2 and BDS-3 Joint Precise Point Positioning with Time Delay Bias Estimation","volume":"31","author":"Jiao","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/navi.296","article-title":"Overview of BDS III New Signals","volume":"66","author":"Lu","year":"2019","journal-title":"Navigation"},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1002\/j.2161-4296.2002.tb00260.x","article-title":"A New Method for Carrier-Phase-Based Precise Point Positioning","volume":"49","author":"Gao","year":"2002","journal-title":"Navigation"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s00190-013-0611-x","article-title":"A Method for Improving Uncalibrated Phase Delay Estimation and Ambiguity-Fixing in Real-Time Precise Point Positioning","volume":"87","author":"Li","year":"2013","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"04014007","DOI":"10.1061\/(ASCE)SU.1943-5428.0000125","article-title":"Efficient Between-Satellite Single-Difference Precise Point Positioning Model","volume":"140","author":"Elsobeiey","year":"2014","journal-title":"J. Surv. Eng."},{"key":"ref_12","unstructured":"Kouba, J. (2022, September 09). A Guide to Using International GNSS Service (IGS) Products. IGS, Available online: http:\/\/igscb.jpl.nasa.gov\/igscb\/resource\/pubs\/UsingIGSProductsVer21.pdf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/PL00012883","article-title":"Precise Point Positioning Using IGS Orbit and Clock Products","volume":"5","author":"Kouba","year":"2001","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1016\/j.asr.2021.09.006","article-title":"Initial Assessment of BDS-3 Precise Point Positioning Service on GEO B2b Signal","volume":"69","author":"Zhang","year":"2022","journal-title":"Adv. Sp. Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Nie, Z., Xu, X., Wang, Z., and Du, J. (2021). Initial Assessment of BDS PPP-B2b Service: Precision of Orbit and Clock Corrections, and PPP Performance. Remote Sens., 13.","DOI":"10.3390\/rs13112050"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s10291-021-01168-1","article-title":"Initial Assessment of the BDS-3 PPP-B2b RTS Compared with the CNES RTS","volume":"25","author":"Tao","year":"2021","journal-title":"GPS Solut."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3242","DOI":"10.1016\/j.asr.2021.06.006","article-title":"Performance Assessment of Real-Time Precise Point Positioning Using BDS PPP-B2b Service Signal","volume":"68","author":"Ren","year":"2021","journal-title":"Adv. Sp. Res."},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"2942","DOI":"10.1016\/j.asr.2018.03.029","article-title":"Evaluation and Analysis of Real-Time Precise Orbits and Clocks Products from Different IGS Analysis Centers","volume":"61","author":"Zhang","year":"2018","journal-title":"Adv. Sp. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5783","DOI":"10.3390\/s150305783","article-title":"Tightly Coupled Integration of Ionosphere-Constrained Precise Point Positioning and Inertial Navigation Systems","volume":"15","author":"Gao","year":"2015","journal-title":"Sensors"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1007\/s00190-017-1029-7","article-title":"Ionospheric and Receiver DCB-Constrained Multi-GNSS Single-Frequency PPP Integrated with MEMS Inertial Measurements","volume":"91","author":"Gao","year":"2017","journal-title":"J. Geod."},{"key":"ref_22","unstructured":"Shin, E.-H. (2005). Estimation Techniques for Low-Cost Inertial Navigation. [Ph.D. Thesis, The University of Calgary]."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1002\/j.2161-4296.1978.tb01335.x","article-title":"Integration of GPS with Inertial Navigation Systems","volume":"25","author":"Cox","year":"1978","journal-title":"Navigation"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/s00190-021-01514-8","article-title":"Multi-GNSS PPP\/INS Tightly Coupled Integration with Atmospheric Augmentation and Its Application in Urban Vehicle Navigation","volume":"95","author":"Gu","year":"2021","journal-title":"J. Geod."},{"key":"ref_25","unstructured":"Le, A.Q., and Lorga, J. (2006, January 26\u201329). Combining Inertial Navigation System With GPS Precise Point Positioning: Flight Test Results. Proceedings of the ION GNSS 2006, Fort Worth, TX, USA."},{"key":"ref_26","unstructured":"Martell, H. (2009, January 22\u201325). Tightly Coupled Processing of Precise Point Position (PPP) and INS Data. Proceedings of the ION GNSS 2009, Savannah, GA, USA."},{"key":"ref_27","unstructured":"Du, S. (2010). Integration of Precise Point Positioning and Low Cost MEMS IMU. [Master\u2019s Thesis, The University of Calgary]."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1007\/s10291-014-0415-3","article-title":"Tightly Coupled Integration of GPS Precise Point Positioning and MEMS-Based Inertial Systems","volume":"19","year":"2015","journal-title":"GPS Solut."},{"key":"ref_29","unstructured":"(2021, October 20). BeiDou Navigation Satellite System Signal in Space Interface Control Document: Precise Point Positioning Service Signal PPP-B2b (Version 1.0), Available online: http:\/\/en.beidou.gov.cn\/SYSTEMS\/ICD\/202008\/P020200803538771492778.pdf."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s10291-016-0527-z","article-title":"Tightly Coupled Integration of Multi-GNSS PPP and MEMS Inertial Measurement Unit Data","volume":"21","author":"Gao","year":"2017","journal-title":"GPS Solut."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"128866","DOI":"10.1109\/ACCESS.2020.3008849","article-title":"BDS PPP\/INS Tight Coupling Method Based on Non-Holonomic Constraint and Zero Velocity Update","volume":"8","author":"Sun","year":"2020","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10291-018-0725-y","article-title":"Odometer, Low-Cost Inertial Sensors, and Four-GNSS Data to Enhance PPP and Attitude Determination","volume":"22","author":"Gao","year":"2018","journal-title":"GPS Solut."},{"key":"ref_33","unstructured":"Witchayangkoon, B. (2000). Elements of GPS Precise Point Positioning. [Ph.D. Thesis, Spatial Information Science and Engineering, University of Maine]."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Pintor, P., Gonz\u00e1lez, E., Senado, A., Bohlig, P., Sperl, A., Henkel, P., Sim\u00f3n, J., Hern\u00e1ndez, C., de Blas, J., and V\u00e1zquez, J. (2022, January 19\u201323). Galileo High Accuracy Service (HAS) Algorithm and Receiver Development and Testing. Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022), Denver, CO, USA.","DOI":"10.33012\/2022.18462"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10291-012-0273-9","article-title":"Modeling and Assessment of Combined GPS\/GLONASS Precise Point Positioning","volume":"17","author":"Cai","year":"2013","journal-title":"GPS Solut."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/978-3-642-37404-3_29","article-title":"GPS\/GLONASS System Bias Estimation and Application in GPS\/GLONASS Combined Positioning","volume":"244","author":"Chen","year":"2013","journal-title":"Lect. Notes Electr. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/14498596.2013.808164","article-title":"A Comparison between GPS-Only and Combined GPS+GLONASS Precise Point Positioning","volume":"58","author":"Choy","year":"2013","journal-title":"J. Spat. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s10291-019-0852-0","article-title":"Influence of Stochastic Modeling for Inter-System Biases on Multi-GNSS Undifferenced and Uncombined Precise Point Positioning","volume":"23","author":"Zhou","year":"2019","journal-title":"GPS Solut."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10291-015-0513-x","article-title":"GPS\/BDS Short-Term ISB Modelling and Prediction","volume":"21","author":"Jiang","year":"2017","journal-title":"GPS Solut."},{"key":"ref_40","unstructured":"Niu, X., Goodall, C., Nassar, S., and El-Sheimy, N. (2016, January 25\u201327). An efficient methodfor evaluating the performance of MEMS IMUs. Proceedings of the Position location and Navigation Symposium, 2006 IEEE\/ION, San Diego, CA, USA."},{"key":"ref_41","unstructured":"Sukkarieh, S. (2000). Low Cost, High Integrity, Aided Inertial Navigation Systems for Autonomous Land Vehicles. [Ph.D. Thesis, University of Sydney]."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s001900050236","article-title":"Adaptive Kalman Filtering for INS\/GPS","volume":"73","author":"Mohamed","year":"1999","journal-title":"J. Geod."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1007\/s00190-015-0818-0","article-title":"Real-Time Retrieval of Precipitable Water Vapor from GPS and BeiDou Observations","volume":"89","author":"Lu","year":"2015","journal-title":"J. Geod."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/s43020-020-0009-x","article-title":"Multi-Constellation GNSS Precise Point Positioning with Multi-Frequency Raw Observations and Dual-Frequency Observations of Ionospheric-Free Linear Combination","volume":"1","author":"An","year":"2020","journal-title":"Satell. Navig."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s00190-015-0802-8","article-title":"Accuracy and Reliability of Multi-GNSS Real-Time Precise Positioning: GPS, GLONASS, BeiDou, and Galileo","volume":"89","author":"Li","year":"2015","journal-title":"J. Geod."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/978-981-10-0940-2_28","article-title":"The Performance Analysis of Multi-System Integrated Precise Point Positioning (PPP)","volume":"390","author":"Huang","year":"2016","journal-title":"Lect. Notes Electr. Eng."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/199\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:56:20Z","timestamp":1760147780000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/199"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,30]]},"references-count":46,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["rs15010199"],"URL":"https:\/\/doi.org\/10.3390\/rs15010199","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,12,30]]}}}