{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T00:47:05Z","timestamp":1774658825646,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,3,7]],"date-time":"2023-03-07T00:00:00Z","timestamp":1678147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Outstanding Postdoctoral Program of Jiangsu Province","award":["2022ZB113"],"award-info":[{"award-number":["2022ZB113"]}]},{"name":"Outstanding Postdoctoral Program of Jiangsu Province","award":["41904022"],"award-info":[{"award-number":["41904022"]}]},{"name":"Outstanding Postdoctoral Program of Jiangsu Province","award":["41974030"],"award-info":[{"award-number":["41974030"]}]},{"name":"Outstanding Postdoctoral Program of Jiangsu Province","award":["MCM20200J01"],"award-info":[{"award-number":["MCM20200J01"]}]},{"name":"National Natural Science Foundation of China","award":["2022ZB113"],"award-info":[{"award-number":["2022ZB113"]}]},{"name":"National Natural Science Foundation of China","award":["41904022"],"award-info":[{"award-number":["41904022"]}]},{"name":"National Natural Science Foundation of China","award":["41974030"],"award-info":[{"award-number":["41974030"]}]},{"name":"National Natural Science Foundation of China","award":["MCM20200J01"],"award-info":[{"award-number":["MCM20200J01"]}]},{"name":"Ministry of Education-China Mobile Research Fund","award":["2022ZB113"],"award-info":[{"award-number":["2022ZB113"]}]},{"name":"Ministry of Education-China Mobile Research Fund","award":["41904022"],"award-info":[{"award-number":["41904022"]}]},{"name":"Ministry of Education-China Mobile Research Fund","award":["41974030"],"award-info":[{"award-number":["41974030"]}]},{"name":"Ministry of Education-China Mobile Research Fund","award":["MCM20200J01"],"award-info":[{"award-number":["MCM20200J01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>An inter-system model for multi-GNSSs (global navigation satellite systems) makes the interoperability among different GNSS constellations possible. In recent years, inter-system models for geodetic receivers have been extensively studied. However, the precise positioning of smartphones suffers from various problems, and the current research mostly focuses on how to achieve the GNSS ambiguity resolution. Based on the research of receiver channel-dependent bias, in this study, we will research the temporal behaviors of differential inter-system bias (DISB) and implement an inter-system model for smartphones. A representative Huawei P40 (HP40) smartphone was used in the experiments, and the results show the following: (1) For the HP40, the frequencies of Code Division Multiple Access (CDMA) systems are free of receiver channel-dependent phase bias, which provides the chances for further interoperability among these systems. However, the code observations of the HP40 are influenced by receiver channel-dependent code bias; it is therefore suggested to set a large initial standard deviation (STD) value for code observations in the positioning. (2) GPS L1\/QZSS L1 and BDS-2 B1I \/BDS-3 B1I are free of phase DISB, and there is obvious phase DISB between GPS L1 and Galileo E1; even so, the valuations are sufficiently stable and the STD is close to 0.005 cycles. However, the phase DISB of GPS L1\/BDS B1I is unstable. (3) For kinematic positioning, when the stable phase DISB is introduced, a 3\u201338.9% improvement in the N\/E\/U directions of the positioning accuracies in the inter-system differencing is achieved compared with the intra-system differencing.<\/jats:p>","DOI":"10.3390\/rs15061476","type":"journal-article","created":{"date-parts":[[2023,3,7]],"date-time":"2023-03-07T03:11:39Z","timestamp":1678158699000},"page":"1476","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Multi-GNSS Differential Inter-System Bias Estimation for Smartphone RTK Positioning: Feasibility Analysis and Performance"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9345-8082","authenticated-orcid":false,"given":"Rui","family":"Shang","sequence":"first","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengfa","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu","family":"Gan","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5566-1450","authenticated-orcid":false,"given":"Ruicheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wang","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2440-8054","authenticated-orcid":false,"given":"Xiaolin","family":"Meng","sequence":"additional","affiliation":[{"name":"Faculty of Architecture, Civil and Transportation Engineering, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1186\/s43020-022-00064-4","article-title":"PPP\u2013RTK functional models formulated with undifferenced and uncombined GNSS observations","volume":"3","author":"Zhang","year":"2022","journal-title":"Satell. Navig."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Yuan, H., He, X., Li, B., and Geng, J. (2023). Best Integer Equivariant Estimation With Quality Control in GNSS RTK for Canyon Environments. IEEE Trans. Aerosp. Electron. Syst., 1\u201315.","DOI":"10.1109\/TAES.2023.3236916"},{"key":"ref_3","unstructured":"Ye, J. (2020). Research on Pedestrian Navigation Algorithm Based on Multi-Sensor Fusion, Chang\u2019an University."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10291-023-01402-y","article-title":"An investigation of PPP time transfer via BDS-3 PPP-B2b service","volume":"27","author":"Ge","year":"2023","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sikirica, N., Mali\u0107, E., Rumora, I., and Filjar, R. (2017, January 21\u201322). Exploitation of Google GNSS measurement API for risk assessment of GNSS applications. Proceedings of the 2017 25th Telecommunication Forum (TELFOR), Belgrade, Serbia.","DOI":"10.1109\/TELFOR.2017.8249343"},{"key":"ref_6","first-page":"43","article-title":"Precise positioning using raw GPS measurements from Android smartphones","volume":"27","author":"Banville","year":"2016","journal-title":"GPS World"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chen, B., Gao, C., Liu, Y., and Sun, P. (2019). Real-time precise point positioning with a Xiaomi MI 8 android smartphone. Sensors, 19.","DOI":"10.3390\/s19122835"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"111078","DOI":"10.1016\/j.measurement.2022.111078","article-title":"A study on the real-time code-based GNSS positioning with Android smartphones","volume":"194","author":"Bahadur","year":"2022","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/s43020-022-00079-x","article-title":"Real-time GNSS precise point positioning with smartphones for vehicle navigation","volume":"3","author":"Li","year":"2022","journal-title":"Satell. Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/s10291-019-0885-4","article-title":"Characteristics of raw multi-GNSS measurement error from Google Android smart devices","volume":"23","author":"Li","year":"2019","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s10291-018-0799-6","article-title":"Real-time carrier phase multipath detection based on dual-frequency C\/N0 data","volume":"23","author":"Zhang","year":"2019","journal-title":"GPS Solut."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2621","DOI":"10.1007\/s00190-019-01323-0","article-title":"On the feasibility of resolving Android GNSS carrier-phase ambiguities","volume":"93","author":"Geng","year":"2019","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Darugna, F., W\u00fcbbena, J., Ito, A., W\u00fcbbena, T., W\u00fcbbena, G., and Schmitz, M. (2019, January 16\u201320). RTK and PPP-RTK using smartphones: From short-baseline to long-baseline applications. Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, FL, USA.","DOI":"10.33012\/2019.17078"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bochkati, M., Sharma, H., Lichtenberger, C.A., and Pany, T. (2020, January 20\u201323). Demonstration of fused RTK (fixed)+ inertial positioning using Android smartphone sensors only. Proceedings of the 2020 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Portland, OR, USA.","DOI":"10.1109\/PLANS46316.2020.9109865"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s10291-021-01181-4","article-title":"A new IMU-aided multiple GNSS fault detection and exclusion algorithm for integrated navigation in urban environments","volume":"25","author":"Sun","year":"2021","journal-title":"GPS Solut."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10291-022-01369-2","article-title":"NLOS signal detection and correction for smartphone using convolutional neural network and variational mode decomposition in urban environment","volume":"27","author":"Liu","year":"2023","journal-title":"GPS Solut."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Xia, Y., Pan, S., Meng, X., Gao, W., Ye, F., Zhao, Q., and Zhao, X. (2020). Anomaly detection for urban vehicle GNSS observation with a hybrid machine learning system. Remote Sens., 12.","DOI":"10.3390\/rs12060971"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1186\/s43020-021-00035-1","article-title":"First results of BDS positioning for LBS applications in the UK","volume":"2","author":"Xia","year":"2021","journal-title":"Satell. Navig."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Humphreys, T.E., Murrian, M., Van Diggelen, F., Podshivalov, S., and Pesyna, K.M. (2016, January 11\u201314). On the feasibility of cm-accurate positioning via a smartphone\u2019s antenna and GNSS chip. Proceedings of the 2016 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Savannah, GR, USA.","DOI":"10.1109\/PLANS.2016.7479707"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Riley, S., Lentz, W., and Clare, A. (2017, January 25\u201329). On the path to precision-observations with android GNSS observables. Proceedings of the 30th International Technical Meeting of The Satellite Division of The Institute of Navigation (ION GNSS+ 2017), Portland, OR, USA.","DOI":"10.33012\/2017.15244"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s10291-019-0892-5","article-title":"Signal characterization and assessment of code GNSS positioning with low-power consumption smartphones","volume":"23","author":"Paziewski","year":"2019","journal-title":"GPS Solut."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"091001","DOI":"10.1088\/1361-6501\/ab8a7d","article-title":"Recent advances and perspectives for positioning and applications with smartphone GNSS observations","volume":"31","author":"Paziewski","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109162","DOI":"10.1016\/j.measurement.2021.109162","article-title":"An analysis of multi-GNSS observations tracked by recent Android smartphones and smartphone-only relative positioning results","volume":"175","author":"Paziewski","year":"2021","journal-title":"Measurement"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1007\/s00190-022-01656-3","article-title":"Android multi-GNSS ambiguity resolution in the case of receiver channel-dependent phase biases","volume":"96","author":"Li","year":"2022","journal-title":"J. Geod."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s00190-022-01652-7","article-title":"Ambiguity resolution for smartphone GNSS precise positioning: Effect factors and performance","volume":"96","author":"Li","year":"2022","journal-title":"J. Geod."},{"key":"ref_26","unstructured":"Julien, O., Alves, P., Cannon, M.E., and Zhang, W. (2003, January 9). A tightly coupled GPS\/GALILEO combination for improved ambiguity resolution. Proceedings of the European Navigation Conference (ENC-GNSS\u201903), Calgary, AB, Canada."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s00190-016-0983-9","article-title":"On the short-term temporal variations of GNSS receiver differential phase biases","volume":"91","author":"Zhang","year":"2017","journal-title":"J. Geod."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1002\/navi.64","article-title":"Differential code bias estimation using multi-GNSS observations and global ionosphere maps","volume":"61","author":"Montenbruck","year":"2014","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/s10291-012-0298-0","article-title":"Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution","volume":"17","author":"Odijk","year":"2013","journal-title":"GPS Solut."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s00190-014-0763-3","article-title":"Accounting for Galileo\u2013GPS inter-system biases in precise satellite positioning","volume":"89","author":"Paziewski","year":"2015","journal-title":"J. Geod."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s10291-015-0450-8","article-title":"Assessing the IRNSS L5-signal in combination with GPS, Galileo, and QZSS L5\/E5a-signals for positioning and navigation","volume":"20","author":"Nadarajah","year":"2016","journal-title":"GPS Solut."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s10291-016-0536-y","article-title":"GPS, Galileo, QZSS and IRNSS differential ISBs: Estimation and application","volume":"21","author":"Odijk","year":"2017","journal-title":"GPS Solut."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1007\/s00190-016-0921-x","article-title":"Single-frequency, dual-GNSS versus dual-frequency, single-GNSS: A low-cost and high-grade receivers GPS-BDS RTK analysis","volume":"90","author":"Odolinski","year":"2016","journal-title":"J. Geod."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Wu, M., Liu, W., Wang, W., and Zhang, X. (2019). Differential inter-system biases estimation and initial assessment of instantaneous tightly combined RTK with BDS-3, GPS, and Galileo. Remote Sens., 11.","DOI":"10.3390\/rs11121430"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2879","DOI":"10.1016\/j.asr.2022.11.021","article-title":"Tight integration of BDS-3\/BDS-2\/GPS\/Galileo observations considering the new overlapping DISBs and its application in obstructed environments","volume":"71","author":"Yuan","year":"2022","journal-title":"Adv. Space Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s10291-017-0687-5","article-title":"Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases","volume":"22","author":"Gao","year":"2018","journal-title":"GPS Solut."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"015009","DOI":"10.1088\/1361-6501\/ab4209","article-title":"Characteristics of GPS, BDS2, BDS3 and Galileo inter-system biases and their influence on RTK positioning","volume":"31","author":"Mi","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s10291-019-0873-8","article-title":"Multi-GNSS inter-system biases: Estimability analysis and impact on RTK positioning","volume":"23","author":"Mi","year":"2019","journal-title":"GPS Solut."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Chen, H., Jiang, W., and Li, J. (2019). Multi-GNSS relative positioning with fixed inter-system ambiguity. Remote Sens., 11.","DOI":"10.3390\/rs11040454"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1017\/S0373463320000077","article-title":"Particle filter-based inter-system positioning model for non-overlapping frequency code division multiple access systems","volume":"73","author":"Shang","year":"2020","journal-title":"J. Navig."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"025009","DOI":"10.1088\/1361-6501\/ab4844","article-title":"Estimability analysis of differential inter-system biases and differential inter-frequency biases for dual-frequency GPS and BDS combined RTK","volume":"31","author":"Liu","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/navi.132","article-title":"Zero-baseline Analysis of GPS\/BeiDou\/Galileo Between-Receiver Differential Code Biases (BR-DCBs): Time-wise Retrieval and Preliminary Characterization","volume":"63","author":"Zhang","year":"2016","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_43","first-page":"1","article-title":"Model and Performance Analysis of Tightly Combined BeiDou B2 and Galileo E5b Relative Positioning for Short Baseline","volume":"45","author":"Xiaohong","year":"2017","journal-title":"Acta Geod. Et Cartogr. Sin."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s00190-022-01660-7","article-title":"A composite stochastic model considering the terrain topography for real-time GNSS monitoring in canyon environments","volume":"96","author":"Zhang","year":"2022","journal-title":"J. Geod."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1018420","DOI":"10.3389\/feart.2022.1018420","article-title":"An optimized stochastic model for smartphone GNSS positioning","volume":"10","author":"Sui","year":"2022","journal-title":"Front. Earth Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"110619","DOI":"10.1016\/j.measurement.2021.110619","article-title":"Stochastic model assessment of low-cost devices considering the impacts of multipath effects and atmospheric delays","volume":"188","author":"Yuan","year":"2022","journal-title":"Measurement"},{"key":"ref_47","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."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/6\/1476\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:49:39Z","timestamp":1760122179000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/6\/1476"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,7]]},"references-count":47,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["rs15061476"],"URL":"https:\/\/doi.org\/10.3390\/rs15061476","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,7]]}}}