{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:36:17Z","timestamp":1778603777835,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T00:00:00Z","timestamp":1635292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development Program of China","award":["2018YFB0505200"],"award-info":[{"award-number":["2018YFB0505200"]}]},{"name":"the National Key Research and Development Program of China","award":["2018YFB0505201"],"award-info":[{"award-number":["2018YFB0505201"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["2042018kf0253"],"award-info":[{"award-number":["2042018kf0253"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Aiming at the GNSS receiver vulnerability in challenging urban environments and low power consumption of integrated navigation systems, an improved robust adaptive Kalman filter (IRAKF) algorithm with real-time performance and low computation complexity for single-frequency GNSS\/MEMS-IMU\/odometer integrated navigation module is proposed. The algorithm obtains the scale factor by the prediction residual, and uses it to adjust the artificially set covariance matrix of the observation vector under different GNSS solution states, so that the covariance matrix of the observation vector changes continuously with the complex scene. Then, the adaptive factor is calculated by the Mahalanobis distance to inflate the state prediction covariance matrix. In addition, the one-step prediction Kalman filter is introduced to reduce the computational complexity of the algorithm. The performance of the algorithm is verified by vehicle experiments in the challenging urban environments. Experiments show that the algorithm can effectively weaken the effects of abnormal model deviations and outliers in the measurements and improve the positioning accuracy of real-time integrated navigation. It can meet the requirements of low power consumption real-time vehicle navigation applications in the complex urban environment.<\/jats:p>","DOI":"10.3390\/rs13214317","type":"journal-article","created":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T23:24:42Z","timestamp":1635377082000},"page":"4317","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["An Improved Adaptive Kalman Filter for a Single Frequency GNSS\/MEMS-IMU\/Odometer Integrated Navigation Module"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9661-3562","authenticated-orcid":false,"given":"Peihui","family":"Yan","sequence":"first","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangning","family":"Zhang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongpeng","family":"Xie","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaji","family":"Wu","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanan","family":"Tang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingnan","family":"Liu","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Grewal, M., Andrews, A., and Bartone, C. (2020). Global Navigation Satellite Systems, Inertial Navigation, and Integration, John Wiley & Sons.","DOI":"10.1002\/9781119547860"},{"key":"ref_2","unstructured":"Kaplan, E.D., and Hegarty, C. (2005). Understanding GPS Principles and Applications, Artech House Publishers."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gallon, E., Joerger, M., and Pervan, B. (2021, January 20\u201324). Development of Stochastic IMU Error Models for INS\/GNSS Integration. Proceedings of Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, MI, USA.","DOI":"10.33012\/2021.17962"},{"key":"ref_4","unstructured":"Shin, E.H. (2005). Estimation Techniques for Low-Cost Inertial Navigation. [Ph.D. Thesis, The University of Calgary]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"28402","DOI":"10.3390\/s151128402","article-title":"Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS\/GPS Integrated Navigation Systems","volume":"15","author":"Hu","year":"2015","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1179\/1752270614Y.0000000099","article-title":"Development and evaluation of GNSS\/INS data processing software for position and orientation systems","volume":"47","author":"Niu","year":"2015","journal-title":"Surv. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/s00190-013-0690-8","article-title":"Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion","volume":"88","author":"Chang","year":"2014","journal-title":"J. Geod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.measurement.2015.11.008","article-title":"Analysis of a robust Kalman filter in loosely coupled GPS\/INS navigation system","volume":"80","author":"Zhao","year":"2016","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jiang, C., Zhang, S.B., and Zhang, Q.Z. (2016). A New Adaptive H-Infinity Filtering Algorithm for the GPS\/INS Integrated Navigation. Sensors, 16.","DOI":"10.3390\/s16122127"},{"key":"ref_10","unstructured":"Teunissen, P.J.G. (1990, January 20\u201323). Quality control in integrated navigation systems. Proceedings of the IEEE Symposium on Position Location and Navigation. A Decade of Excellence in the Navigation Sciences, Las Vegas, NV, USA."},{"key":"ref_11","first-page":"1","article-title":"A Novel Robust Interval Kalman Filter Algorithm for GPS\/INS Integrated Navigation","volume":"2016","author":"Jiang","year":"2016","journal-title":"J. Sens."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Jiang, C., and Zhang, S.B. (2018). A Novel Adaptively-Robust Strategy Based on the Mahalanobis Distance for GPS\/INS Integrated Navigation Systems. Sensors, 18.","DOI":"10.3390\/s18030695"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Gao, B., Hu, G., Zhu, X., and Zhong, Y. (2019). A Robust Cubature Kalman Filter with Abnormal Observations Identification Using the Mahalanobis Distance Criterion for Vehicular INS\/GNSS Integration. Sensors, 19.","DOI":"10.3390\/s19235149"},{"key":"ref_14","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_15","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1017\/S0373463303002248","article-title":"An Adaptive Kalman Filter Based on Sage Windowing Weights and Variance Components","volume":"56","author":"Yang","year":"2003","journal-title":"J. Navig."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","unstructured":"Wang, J., Stewart, M.P., and Tsakiri, M. (2000). Adaptive Kalman Filtering for Integration of GPS with GLONASS and INS, Springer.","DOI":"10.1007\/978-3-642-59742-8_53"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1109\/TSP.2009.2039731","article-title":"Robust Kalman Filter Based on a Generalized Maximum-Likelihood-Type Estimator","volume":"58","author":"Gandhi","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1016\/j.automatica.2006.06.004","article-title":"Robust H2 and H\u221e filtering for uncertain linear systems","volume":"42","author":"Duan","year":"2006","journal-title":"Automatica"},{"key":"ref_20","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_21","doi-asserted-by":"crossref","unstructured":"Zhao, L., and Liu, J. (August, January 31). An Improved Adaptive Filtering Algorithm with Applications in Integrated Navigation. Proceedings of the 2012 Third International Conference on Digital Manufacturing & Automation, Guilin, China.","DOI":"10.1109\/ICDMA.2012.44"},{"key":"ref_22","unstructured":"Shi, E. (2012, January 18\u201320). An Improved Real-Time Adaptive Kalman Filter for Low-Cost Integrated GPS\/INS Navigation. Proceedings of the 2012 International Conference on Measurement, Information and Control, Harbin, China."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1179\/003962608X325330","article-title":"Adaptively robust filter with multi adaptive factors","volume":"40","author":"Yang","year":"2013","journal-title":"Surv. Rev."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Yang, Y. (2010). Adaptively Robust Kalman Filters with Applications in Navigation. Sciences of Geodesy-I, Springer.","DOI":"10.1007\/978-3-642-11741-1_2"},{"key":"ref_26","unstructured":"Yang, Y., Xu, T., and Xu, J. (2011, January 13\u201315). Principles and Comparisons of Various Adaptively Robust Filters with Applications in Geodetic Positioning. Proceedings of the 1st International Workshop on the Quality of Geodetic Observation and Monitoring Systems (QuGOMS\u201911), Munich, Germany."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2539","DOI":"10.1109\/LRA.2018.2808368","article-title":"Perception, Guidance, and Navigation for Indoor Autonomous Drone Racing Using Deep Learning","volume":"3","author":"Jung","year":"2018","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Rostami, M., Kolouri, S., Eaton, E., and Kim, K. (2019, January 16\u201317). SAR Image Classification Using Few-Shot Cross-Domain Transfer Learning. Proceedings of the 2019 IEEE\/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), Long Beach, CA, USA.","DOI":"10.1109\/CVPRW.2019.00120"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Abdallah, A., and Kassas, Z. (2020). Deep Learning-Aided Spatial Discrimination for Multipath Mitigation, IEEE.","DOI":"10.1109\/PLANS46316.2020.9109935"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Fayjie, A., Hossain, S., Doukhi, O., and Lee, D. (July, January 28). Driverless Car: Autonomous Driving Using Deep Reinforcement Learning in Urban Environment. Proceedings of the 2018 15th International Conference on Ubiquitous Robots (UR), Jeju, Korea.","DOI":"10.1109\/URAI.2018.8441797"},{"key":"ref_31","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_32","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_33","doi-asserted-by":"crossref","unstructured":"Simon, D. (2006). Optimal State Estimation (Kalman, H\u221e, and Nonlinear Approaches)||Optimal Smoothing, John Wiley and Sons.","DOI":"10.1002\/0470045345"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"541","DOI":"10.4028\/www.scientific.net\/AMM.182-183.541","article-title":"A Rapid Computation Method for Kalman Filtering in Vehicular SINS\/GPS Integrated System","volume":"182\u2013183","author":"Zhu","year":"2012","journal-title":"Appl. Mech. Mater."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0373463318000140","article-title":"A Low Complexity Integrated Navigation System for Underwater Vehicles","volume":"71","author":"Emami","year":"2018","journal-title":"J. Navig."},{"key":"ref_36","first-page":"1","article-title":"Efficiency Improvement of Kalman Filter for GNSS\/INS through One-Step Prediction of P Matrix","volume":"2015","author":"Li","year":"2015","journal-title":"Math. Probl. Eng."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/21\/4317\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:24:40Z","timestamp":1760167480000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/21\/4317"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,27]]},"references-count":36,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["rs13214317"],"URL":"https:\/\/doi.org\/10.3390\/rs13214317","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,27]]}}}