{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T18:28:34Z","timestamp":1772303314894,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T00:00:00Z","timestamp":1690329600000},"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":["2021YFB2501102"],"award-info":[{"award-number":["2021YFB2501102"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Modern navigation systems are inseparable from an integrated solution consisting of a global navigation satellite system (GNSS) and an inertial navigation system (INS) since they serve as an important cornerstone of national comprehensive positioning, navigation, and timing (PNT) technology and can provide position, velocity, and attitude information at higher accuracy and better reliability. A robust adaptive method utilizes the observation information of both systems to optimize the filtering system, overcoming the shortcomings of the Kalman filter (KF) in complex urban environments. We propose a novel robust adaptive scheme based on a multi-condition decision model suitable for tightly coupled real-time kinematic (RTK)\/INS architecture, which can reasonably determine whether the filtering system performs robust estimation (TCRKF) or adaptive filtering (TCAKF), improving the robust estimation method of two factors considering ambiguity variance for RTK-related observations. The performance of the proposed robust adaptive algorithm was evaluated through two sets of real vehicle tests. Compared with the TCAKF and TCRKF algorithms, the new robust adaptive scheme improves the average three-dimensional (3D) position root mean square (RMS) by 31% and 18.88%, respectively. It provides better accuracy and reliability for position, velocity, and attitude simultaneously.<\/jats:p>","DOI":"10.3390\/rs15153725","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T02:07:17Z","timestamp":1690423637000},"page":"3725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Novel Optimal Robust Adaptive Scheme for Accurate GNSS RTK\/INS Tightly Coupled Integration in Urban Environments"],"prefix":"10.3390","volume":"15","author":[{"given":"Jiaji","family":"Wu","sequence":"first","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0122-5514","authenticated-orcid":false,"given":"Jinguang","family":"Jiang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"},{"name":"Hubei Luojia Laboratory, Wuhan University, Wuhan 430079, China"},{"name":"School of Microelectronics, Wuhan University, Wuhan 430079, China"}]},{"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}]},{"given":"Yuying","family":"Li","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9661-3562","authenticated-orcid":false,"given":"Peihui","family":"Yan","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}]},{"given":"Xiaoliang","family":"Meng","sequence":"additional","affiliation":[{"name":"School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1017\/S0373463318000644","article-title":"Performance Evaluation of Kinematic BDS\/GNSS Real-Time Precise Point Positioning for Maritime Positioning","volume":"72","author":"Yang","year":"2019","journal-title":"J. Navig."},{"key":"ref_2","first-page":"832","article-title":"A Precise Point Timing Method Based on BDS-3 B2b Signal","volume":"50","author":"Yi","year":"2022","journal-title":"Acta Electron. Sin."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107836","DOI":"10.1016\/j.measurement.2020.107836","article-title":"Performance of ionospheric-free PPP time transfer models with BDS-3 quad-frequency observations","volume":"160","author":"Ge","year":"2020","journal-title":"Measurement"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1007\/s10291-017-0601-1","article-title":"New optimal smoothing scheme for improving relative and absolute accuracy of tightly coupled GNSS\/SINS integration","volume":"21","author":"Zhang","year":"2017","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10291-006-0050-8","article-title":"GPS\/MEMS INS integrated system for navigation in urban areas","volume":"11","author":"Godha","year":"2007","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Yan, P., Jiang, J., Zhang, F., Xie, D., Wu, J., Zhang, C., Tang, Y., and Liu, J. (2021). An Improved Adaptive Kalman Filter for a Single Frequency GNSS\/MEMS-IMU\/Odometer Integrated Navigation Module. Remote Sens., 13.","DOI":"10.3390\/rs13214317"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"02013","DOI":"10.1051\/e3sconf\/202020602013","article-title":"Performance analysis of GNSS\/INS loosely coupled integration systems under GNSS signal blocking environment","volume":"206","author":"Wang","year":"2020","journal-title":"E3S Web Conf."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, W., Li, W., Cui, X., Zhao, S., and Lu, M. (2018). A Tightly Coupled RTK\/INS Algorithm with Ambiguity Resolution in the Position Domain for Ground Vehicles in Harsh Urban Environments. Sensors, 18.","DOI":"10.3390\/s18072160"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"14997","DOI":"10.1109\/JSEN.2021.3073963","article-title":"Cubature Kalman filter with both adaptability and robustness for tightly-coupled GNSS\/INS integration","volume":"21","author":"Gao","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, L., Viktorovich, P.A., Selezneva, M.S., and Neusypin, K.A. (2021). Adaptive Estimation Algorithm for Correcting Low-Cost MEMS-SINS Errors of Unmanned Vehicles under the Conditions of Abnormal Measurements. Sensors, 21.","DOI":"10.3390\/s21020623"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1007\/s12239-022-0142-7","article-title":"GNSS\/INS Tightly Coupled Navigation with Robust Adaptive Extended Kalman Filter","volume":"23","author":"Wu","year":"2022","journal-title":"Int. J. Automot. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"157241","DOI":"10.1109\/ACCESS.2019.2946981","article-title":"Kinematic Measurement of the Railway Track Centerline Position by GNSS\/INS\/Odometer Integration","volume":"7","author":"Zhou","year":"2019","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yan, P., Jiang, J., Tang, Y., Zhang, F., Xie, D., Wu, J., Liu, J., and Liu, J. (2021). Dynamic Adaptive Low Power Adjustment Scheme for Single-Frequency GNSS\/MEMS-IMU\/Odometer Integrated Navigation in the Complex Urban Environment. Remote Sens., 13.","DOI":"10.3390\/rs13163236"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104120","DOI":"10.1016\/j.trc.2023.104120","article-title":"An automated driving systems data acquisition and analytics platform","volume":"151","author":"Xia","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_15","first-page":"1","article-title":"HYDRO-3D: Hybrid Object Detection and Tracking for Cooperative Perception Using 3D LiDAR","volume":"99","author":"Zonglin","year":"2023","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8085","DOI":"10.1109\/JSTARS.2022.3206399","article-title":"YOLOv5-Tassel: Detecting Tassels in RGB UAV Imagery with Improved YOLOv5 Based on Transfer Learning","volume":"15","author":"Liu","year":"2022","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107993","DOI":"10.1016\/j.ymssp.2021.107993","article-title":"Estimation on IMU yaw misalignment by fusing information of automotive onboard sensors","volume":"162","author":"Xia","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"012019","DOI":"10.1088\/1757-899X\/187\/1\/012019","article-title":"Investigation of adaptive robust Kalman filtering algorithms for GPS\/DR navigation system filters","volume":"187","author":"Elzoghby","year":"2017","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"035107","DOI":"10.1088\/1361-6501\/aca421","article-title":"An improved GNSS\/INS navigation method based on cubature Kalman filter for occluded environment","volume":"34","author":"Liu","year":"2022","journal-title":"Meas. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Xu, Y., Wang, K., Jiang, C., Li, Z., Yang, C., Liu, D., and Zhang, H. (2023). Motion-Constrained GNSS\/INS Integrated Navigation Method Based on BP Neural Network. Remote Sens., 15.","DOI":"10.3390\/rs15010154"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yu, H., Han, H., Wang, J., Xiao, H., and Wang, C. (2020). Single-Frequency GPS\/BDS RTK and INS Ambiguity Resolution and Positioning Performance Enhanced with Positional Polynomial Fitting Constraint. Remote Sens., 12.","DOI":"10.3390\/rs12152374"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s00190-010-0374-6","article-title":"Robust Kalman filtering with constraints: A case study for integrated navigation","volume":"84","author":"Yang","year":"2010","journal-title":"J. Geod."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s10291-021-01185-0","article-title":"Improved forward and backward adaptive smoothing algorithm","volume":"26","author":"Lin","year":"2022","journal-title":"GPS Solut."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.4028\/www.scientific.net\/AMM.284-287.1956","article-title":"The Performance Analysis of an AKF Based Tightly-Coupled INS\/GNSS Sensor Fusion Scheme with Non-Holonomic Constraints for Land Vehicular Applications","volume":"284\u2013287","author":"Chiang","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1109\/TCST.2022.3174511","article-title":"Autonomous Vehicle Kinematics and Dynamics Synthesis for Sideslip Angle Estimation Based on Consensus Kalman Filter","volume":"31","author":"Xia","year":"2023","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"21675","DOI":"10.1109\/JSEN.2021.3059050","article-title":"Automated Vehicle Sideslip Angle Estimation Considering Signal Measurement Characteristic","volume":"21","author":"Wei","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"10668","DOI":"10.1109\/TVT.2020.2983738","article-title":"IMU-Based Automated Vehicle Body Sideslip Angle and Attitude Estimation Aided by GNSS Using Parallel Adaptive Kalman Filters","volume":"69","author":"Xiong","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1049\/iet-its.2019.0826","article-title":"Vision-aided Intelligent Vehicle Sideslip Angle Estimation Based on Dynamic Model","volume":"14","author":"Liu","year":"2020","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wen, W., Kan, Y.C., and Hsu, L.T. (2019, January 16\u201320). Performance comparison of GNSS\/INS integrations based on EKF and factor graph optimization. Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Miami, FL, USA.","DOI":"10.33012\/2019.17129"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Falco, G., Pini, M., and Marucco, G. (2017). Loose and tight GNSS\/INS integrations: Comparison of performance assessed in real urban scenarios. Sensors, 17.","DOI":"10.3390\/s17020255"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, Y., Mi, J., Xu, Y., Li, B., Jiang, D., and Liu, W. (2022). A Robust Adaptive Filtering Algorithm for GNSS Single-Frequency RTK of Smartphone. Remote Sens., 14.","DOI":"10.3390\/rs14246388"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1007\/s10291-022-01331-2","article-title":"Improving the combined GNSS\/INS positioning by using tightly integrated RTK","volume":"26","author":"Li","year":"2022","journal-title":"GPS Solut."},{"key":"ref_33","unstructured":"Yang, Y. (2017). Adaptive Navigation and Kinematic Positioning, SinoMaps. [2nd ed.]."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s001900000157","article-title":"Adaptively robust filtering for kinematic geodetic positioning","volume":"75","author":"Yang","year":"2001","journal-title":"J. Geod."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Dong, Y., Wang, D., Zhang, L., Li, Q., and Wu, J. (2020). Tightly Coupled GNSS\/INS Integration with Robust Sequential Kalman Filter for Accurate Vehicular Navigation. Sensors, 20.","DOI":"10.3390\/s20020561"},{"key":"ref_36","first-page":"478","article-title":"Performance Analysis of Tightly Coupled RTK\/INS Algorithm in Case of Insufficient Number of Satellites","volume":"43","author":"Li","year":"2018","journal-title":"Geomat. Inf. Wuhan Univ."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Shi, B., Wang, M., Wang, Y., Bai, Y., Lin, K., and Yang, F. (2021). Effect analysis of GNSS\/INS processing strategy for sufficient utilization of urban environment observations. Sensors, 21.","DOI":"10.3390\/s21020620"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Qiao, S., Fan, Y., Wang, G., Mu, D., and He, Z. (2022). Radar Target Tracking for Unmanned Surface Vehicle Based on Square Root Sage\u2013Husa Adaptive Robust Kalman Filter. Sensors, 22.","DOI":"10.3390\/s22082924"},{"key":"ref_39","first-page":"76","article-title":"Application of Sage-Husa filter considering innovation vectors in mobile phone GNSS location","volume":"8","author":"Peng","year":"2020","journal-title":"J. Navig. Position."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Zhao, X., Qian, Y., Zhang, M., Niu, J., and Kou, Y. (2011, January 7\u201310). An improved adaptive Kalman filtering algorithm for advanced robot navigation system based on GPS\/INS. Proceedings of the 2011 IEEE International Conference on Mechatronics and Automation, Beijing, China.","DOI":"10.1109\/ICMA.2011.5985803"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"105110","DOI":"10.1088\/1361-6501\/ac0370","article-title":"Improved robust and adaptive filter based on non-holonomic constraints for RTK\/INS integrated navigation","volume":"32","author":"Yang","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Li, T., Zhang, H., Niu, X., and Gao, Z. (2017). Tightly-Coupled Integration of Multi-GNSS Single-Frequency RTK and MEMS-IMU for Enhanced Positioning Performance. Sensors, 17.","DOI":"10.3390\/s17112462"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Li, T., Zhang, H., Gao, Z., Chen, Q., and Niu, X. (2018). High-Accuracy Positioning in Urban Environments Using Single-Frequency Multi-GNSS RTK\/MEMS-IMU Integration. Remote Sens., 10.","DOI":"10.3390\/rs10020205"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TIM.2007.908635","article-title":"Analysis and modeling of inertial sensors using Allan variance","volume":"57","author":"Hou","year":"2008","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1009","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_46","unstructured":"Jiahao, W. (2019). Research on GNSS RTK\/INS\/Vehicle Auxiliary Information Tightly-Coupled Multi-Source Navigation and Positioning Algorithm. [Master\u2019s Thesis, Wuhan University]."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Hsu, L.T., Kubo, N., Wen, W., Chen, W., Liu, Z., Suzuki, T., and Meguro, J. (2021, January 20\u201324). UrbanNav: An open-sourced multisensory dataset for benchmarking positioning algorithms designed for urban areas. Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, MO, USA.","DOI":"10.33012\/2021.17895"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/15\/3725\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:19:17Z","timestamp":1760127557000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/15\/3725"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,26]]},"references-count":47,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["rs15153725"],"URL":"https:\/\/doi.org\/10.3390\/rs15153725","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,26]]}}}