{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T05:32:48Z","timestamp":1780378368906,"version":"3.54.1"},"reference-count":54,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T00:00:00Z","timestamp":1683244800000},"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":["2017YFC0821102"],"award-info":[{"award-number":["2017YFC0821102"]}]},{"name":"National Key Research and Development Program of China","award":["2016YFB0502004"],"award-info":[{"award-number":["2016YFB0502004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The resolution accuracy of the inertial navigation system\/global navigation satellite system (INS\/GNSS) integrated system would be degraded in challenging areas. This paper proposed a novel algorithm, which combines the second-order mutual difference method with the maximum correntropy criteria extended Kalman filter to address the following problems (1) the GNSS measurement noise estimation cannot be isolated from the state estimation and suffers from the auto-correlated statistic sequences, and (2) the performance of EKF would be degraded under the non-Gaussian condition. In detail, the proposed algorithm determines the possible distribution of the measurement noise by a kernel density function detection, then depending on the detection result, either the difference sequences\u2013based method or an autoregressive correction algorithm\u2019s result is utilized for calculating the noise covariance. Then, the obtained measurement noise covariance is used in MCEKF instead of EKF to enhance filter adaptiveness. Meanwhile, to enhance the numerical stability of the MCEKF, we adopted the Cholesky decomposition to calculate the matrix inverse in the kernel function. The road experiment verified that our proposed method could achieve more accurate navigation resolutions than the compared ones.<\/jats:p>","DOI":"10.3390\/rs15092430","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T09:18:09Z","timestamp":1683278289000},"page":"2430","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Redundant Measurement-Based Maximum Correntropy Extended Kalman Filter for the Noise Covariance Estimation in INS\/GNSS Integration"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3319-3593","authenticated-orcid":false,"given":"Dapeng","family":"Wang","sequence":"first","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hai","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"},{"name":"Science and Technology on Aircraft Control Laboratory, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5676-0071","authenticated-orcid":false,"given":"Hongliang","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7570-3948","authenticated-orcid":false,"given":"Baoshuang","family":"Ge","sequence":"additional","affiliation":[{"name":"Yancheng State-Owned Assets Investment Group Co., Ltd., No. 669 Century Avenue, Yandu District, Yancheng 224000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, H., Wu, W., Zhang, S., Wu, C., and Zhong, R. (2023). A GNSS\/LiDAR\/IMU Pose Estimation System Based on Collaborative Fusion of Factor Map and Filtering. Remote Sens., 15.","DOI":"10.3390\/rs15030790"},{"key":"ref_2","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_3","doi-asserted-by":"crossref","unstructured":"Li, Z., Zhang, H., Zhou, Q., and Che, H. (2017). An Adaptive Low-Cost INS\/GNSS Tightly-Coupled Integration Architecture Based on Redundant Measurement Noise Covariance Estimation. Sensors, 17.","DOI":"10.3390\/s17092032"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Fang, W., Jiang, J., Lu, S., Gong, Y., Tao, Y., Tang, Y., Yan, P., Luo, H., and Liu, J. (2020). A LSTM Algorithm Estimating Pseudo Measurements for Aiding INS during GNSS Signal Outages. Remote Sens., 12.","DOI":"10.3390\/rs12020256"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.inffus.2018.04.006","article-title":"Multi-sensor fusion methodology for enhanced land vehicle positioning","volume":"46","author":"Li","year":"2019","journal-title":"Inf. Fusion"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"6818","DOI":"10.1109\/JSEN.2022.3150073","article-title":"Improved Vehicle Localization Using On-Board Sensors and Vehicle Lateral Velocity","volume":"22","author":"Gao","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_8","unstructured":"Groves, P.D. (2008). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1109\/TCST.2022.3174511","article-title":"Autonomous Vehicle Kinematics and Dynamics Synthesis for Sideslip AngleEstimation Based on Consensus Kalman Filter","volume":"31","author":"Xia","year":"2022","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_10","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_11","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":"Liu","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MAES.2020.3002001","article-title":"State estimation methods in navigation: Overview and application","volume":"35","author":"Biswas","year":"2020","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"11090","DOI":"10.1109\/ACCESS.2022.3146732","article-title":"A Review of Dynamic Phasor Estimation by Non-Linear Kalman Filters","volume":"10","author":"Khodaparast","year":"2022","journal-title":"IEEE Access"},{"key":"ref_14","unstructured":"Bar-Shalom, Y., Li, X.R., and Kirubarajan, T. (2004). Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software, John Wiley & Sons."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/JPROC.2003.823141","article-title":"Unscented filtering and nonlinear estimation","volume":"92","author":"Julier","year":"2004","journal-title":"Proc. IEEE."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","article-title":"Cubature kalman filters","volume":"54","author":"Arasaratnam","year":"2009","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Huang, H., and Zhang, H. (2022). Student\u2019s t-Kernel-Based Maximum Correntropy Kalman Filter. Sensors, 22.","DOI":"10.3390\/s22041683"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"119","DOI":"10.23919\/SAIEE.2015.8531938","article-title":"A Study on Impulse Noise and Its Models","volume":"106","author":"Shongwe","year":"2015","journal-title":"SAIEE Afr. Res. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1109\/18.761256","article-title":"Non-Gaussian noise models in signal processing for telecommunications: New methods and results for class A and class B noise models","volume":"45","author":"Middleton","year":"1999","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2317","DOI":"10.1109\/TPWRD.2013.2273942","article-title":"A markov-middleton model for bursty impulsive noise: Modeling and receiver design","volume":"28","author":"Ndo","year":"2013","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2145","DOI":"10.3390\/rs5052145","article-title":"SAR Images Statistical Modeling and Classification Based on the Mixture of Alpha-Stable Distributions","volume":"5","author":"Peng","year":"2013","journal-title":"Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Wang, J., Li, Z., Zhao, Y., Wang, R., and Habib, A. (2022). Optimization Method of Airborne LiDAR Individual Tree Segmentation Based on Gaussian Mixture Model. Remote Sens., 14.","DOI":"10.3390\/rs14236167"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2020.3021224","article-title":"MM estimation-based robust cubature Kalman filter for INS\/GPS integrated navigation system","volume":"70","author":"Guangcai","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1049\/iet-smt.2011.0169","article-title":"Huber-based novel robust unscented Kalman filter","volume":"6","author":"Chang","year":"2012","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.automatica.2016.10.004","article-title":"Maximum correntropy Kalman filter","volume":"76","author":"Chen","year":"2017","journal-title":"Automatica"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Principe, J.C. (2010). Information Theoretic Learning: Renyi\u2019s Entropy and Kernel Perspectives, Springer Science & Business Media.","DOI":"10.1007\/978-1-4419-1570-2"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Qu, H., Wang, M., Zhao, J., Zhao, S., Li, T., and Yue, P. (2022). Generalized Asymmetric Correntropy for Robust Adaptive Filtering: A Theoretical and Simulation Study. Remote Sens., 14.","DOI":"10.3390\/rs14153677"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Liao, T., Hirota, K., Wu, X., Shao, S., and Dai, Y. (2022). A Dynamic Self-Tuning Maximum Correntropy Kalman Filter forWireless Sensors Networks Positioning Systems. Remote Sens., 14.","DOI":"10.3390\/rs14174345"},{"key":"ref_30","unstructured":"Wang, S.Y., and Yang, J.Z. (2021, January 8\u201310). State Estimation under Outliers by the Maximum Correntropy Extended Kalman Filter. Proceedings of the 2021 60th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), Tokyo, Japan."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Wang, D., Zhang, H., and Ge, B. (2021). Adaptive Unscented Kalman Filter for Target Tacking with Time-Varying Noise Covariance Based on Multi-Sensor Information Fusion. Sensors, 21.","DOI":"10.3390\/s21175808"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhang, S. (2009, January 19\u201320). An Adaptive Unscented Kalman Filter for Dead Reckoning Systems. Proceedings of the 2009 International Conference on Information Engineering and Computer Science, Wuhan, China.","DOI":"10.1109\/ICIECS.2009.5365064"},{"key":"ref_33","first-page":"1997","article-title":"Strong tracking Kalman filter for non-Gaussian observation","volume":"36","author":"Lu","year":"2019","journal-title":"Kongzhi Lilun Yu Yingyong\/Control Theory Appl."},{"key":"ref_34","first-page":"1482","article-title":"Motion estimation for non-cooperative target based on strong tracking cubature Kalman filter","volume":"51","author":"Xie","year":"2021","journal-title":"Jilin Daxue Xuebao J. Jilin Univ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"108170","DOI":"10.1016\/j.measurement.2020.108170","article-title":"Adaptive H-infinity Kalman filter based random drift modeling and compensation method for ring laser gyroscope","volume":"167","author":"Wang","year":"2021","journal-title":"Measurement"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1109\/JSEN.2011.2107896","article-title":"Random weighting method for multisensory data fusion","volume":"11","author":"Gao","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1002\/acs.2467","article-title":"Windowing and random weighting-based adaptive unscented Kalman filter","volume":"29","author":"Gao","year":"2015","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.ast.2017.08.020","article-title":"Adaptive unscented Kalman filter based on maximum posterior estimation and random weighting","volume":"71","author":"Gao","year":"2017","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2693","DOI":"10.1109\/JSEN.2022.3229475","article-title":"An Optimal Fusion Method of Multiple Inertial Measurement Units Based on Measurement Noise Variance Estimation","volume":"23","author":"Huang","year":"2023","journal-title":"IEEE Sens."},{"key":"ref_40","unstructured":"Velazquez, J.R. (2020). Analysis and Development of Algorithms for Data Fusion in Sensor Arrays. [Ph.D. Thesis, Universit Montpellier]."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Srinivas, P., and Kumar, A. (2017, January 26\u201327). Overview of architecture for GPS-INS integration. Proceedings of the 2017 Recent Developments in Control, Automation & Power Engineering, Noida, India.","DOI":"10.1109\/RDCAPE.2017.8358310"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Xu, X., Nie, Z., Wang, Z., Wang, B., and Du, Q. (2022). Performance Assessment of BDS-3 PPP-B2b\/INS Loosely Coupled Integration. Remote Sens., 14.","DOI":"10.3390\/rs14132957"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Zhai, R., and Yuan, Y. (2022). A Method of Vision Aided GNSS Positioning Using Semantic Information in Complex Urban Environment. Remote Sens., 14.","DOI":"10.3390\/rs14040869"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"10599","DOI":"10.3390\/s130810599","article-title":"The performance analysis of a real-time integrated INS\/GPS vehicle navigation system with abnormal GPS measurement elimination","volume":"13","author":"Chiang","year":"2013","journal-title":"Sensors"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.sigpro.2015.07.014","article-title":"Performance evaluation of Cubature Kalman filter in a GPS\/IMU tightly-coupled navigation system","volume":"119","author":"Zhao","year":"2016","journal-title":"Signal Proc."},{"key":"ref_46","unstructured":"Kong, X., Nebot, E.M., and Durrant-Whyte, H. (1999, January 10\u201315). Development of a nonlinear psi-angle model for large misalignment errors and its application in INS alignment and calibration. Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Detroit, MI, USA."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1109\/TSP.2006.872524","article-title":"Generalized correlation function: Definition, properties, and application to blind equalization","volume":"54","author":"Pokharel","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_48","first-page":"6325","article-title":"Maximum Correntropy Criterion for Robust TOA-Based Localization in NLOS Environments. Circuits Syst","volume":"40","author":"Xiong","year":"2021","journal-title":"Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Mohiuddin, S.M., and Qi, J. (2019, January 4\u20138). Maximum Correntropy Extended Kalman Filtering for Power System Dynamic State Estimation. Proceedings of the IEEE Power & Energy Society General Meeting (PESGM), Atlanta, GA, USA.","DOI":"10.1109\/PESGM40551.2019.8973525"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Ge, B.S., Zhang, H., Fu, W.X., and Yang, J.B. (2020). Enhanced Redundant Measurement-Based Kalman Filter for Measurement Noise Covariance Estimation in INS\/GNSS Integration. Remote Sens., 12.","DOI":"10.3390\/rs12213500"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.pmcj.2017.06.008","article-title":"Improved vehicle positioning algorithm using enhanced innovation-based adaptive Kalman filter","volume":"40","author":"Ghaleb","year":"2017","journal-title":"Pervasive Mob. Comput."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"14247","DOI":"10.1109\/TVT.2020.3038646","article-title":"GPS L1CA\/BDS B1I Multipath Channel Measurements and Modeling for Dynamic Land Vehicle in Shanghai Dense Urban Area","volume":"69","author":"Chen","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Xia, X., Meng, Z., Han, X., Li, H., Tsukiji, T., Xu, R., Zhang, Z., and Ma, J. (2022). Automated Driving Systems Data Acquisition and Processing Platform. arXiv.","DOI":"10.1016\/j.trc.2023.104120"},{"key":"ref_54","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."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/9\/2430\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:29:52Z","timestamp":1760124592000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/9\/2430"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,5]]},"references-count":54,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["rs15092430"],"URL":"https:\/\/doi.org\/10.3390\/rs15092430","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,5]]}}}