{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:32:48Z","timestamp":1774276368113,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,5,16]],"date-time":"2021-05-16T00:00:00Z","timestamp":1621123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41874006"],"award-info":[{"award-number":["41874006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41974026"],"award-info":[{"award-number":["41974026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005195","name":"China University of Mining and Technology","doi-asserted-by":"publisher","award":["2020WLJCRCZL052"],"award-info":[{"award-number":["2020WLJCRCZL052"]}],"id":[{"id":"10.13039\/501100005195","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012154","name":"Graduate Research and Innovation Projects of Jiangsu Province","doi-asserted-by":"publisher","award":["KYCX20_2058"],"award-info":[{"award-number":["KYCX20_2058"]}],"id":[{"id":"10.13039\/501100012154","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In complex urban environments, a single Global Navigation Satellite System (GNSS) is often not ideal for navigation due to a lack of sufficient visible satellites. Additionally, the heading angle error of a GNSS\/micro-electro-mechanical system\u2013grade inertial measurement unit (MIMU) tightly coupled integration based on the single antenna is large, and the attitude angle, velocity, and position calculated therein all have large errors. Considering the above problems, this paper designs a tightly coupled integration of GNSS\/MIMU based on two GNSS antennas and proposes a singular value decomposition (SVD)-based robust adaptive cubature Kalman filter (SVD-RACKF) according to the model characteristics of the integration. In this integration, the high-accuracy heading angle of the carrier is obtained through two antennas, and the existing attitude angle information is used as the observation to constrain the filtering estimation. The proposed SVD-RACKF uses SVD to stabilize the numerical accuracy of the recursive filtering. Furthermore, the three-stage equivalent weight function and the adaptive adjustment factor are constructed to suppress the influence of the gross error and the abnormal state on the parameter estimation, respectively. A set of real measured data was employed for testing and analysis. The results show that dual antennas and dual systems can improve the positioning performance of the integrated system to a certain extent, and the proposed SVD-RACKF can accurately detect the gross errors of the observations and effectively suppress them. Compared with the cubature Kalman filter, the proposed filtering algorithm is more robust, with higher accuracy and reliability of parameter estimation.<\/jats:p>","DOI":"10.3390\/rs13101943","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T02:31:34Z","timestamp":1621218694000},"page":"1943","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Robust Adaptive Cubature Kalman Filter Based on SVD for Dual-Antenna GNSS\/MIMU Tightly Coupled Integration"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3948-9558","authenticated-orcid":false,"given":"Cheng","family":"Pan","sequence":"first","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nijia","family":"Qian","sequence":"additional","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zengke","family":"Li","sequence":"additional","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingxiang","family":"Gao","sequence":"additional","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0237-3663","authenticated-orcid":false,"given":"Zhenbin","family":"Liu","sequence":"additional","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kefan","family":"Shao","sequence":"additional","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s10291-015-0511-z","article-title":"PPP\/INS tightly coupled navigation using adaptive federated filter","volume":"21","author":"Li","year":"2017","journal-title":"GPS Solut."},{"key":"ref_2","unstructured":"Yang, Y. (2008). Tightly Coupled MEMS INS\/GPS Integration with INS Aided Receiver Tracking Loops. [Ph.D. Thesis, University of Calgary]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"106222","DOI":"10.1016\/j.ymssp.2019.07.003","article-title":"Dual-optimization for a MEMS-INS\/GPS system during GPS outages based on the cubature Kalman filter and neural networks","volume":"133","author":"Shen","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/s10291-020-01023-9","article-title":"A low-cost integrated MEMS-based INS\/GPS vehicle navigation system with challenging conditions based on an optimized IT2FNN in occluded environments","volume":"24","author":"Abdolkarimi","year":"2020","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/s10291-020-01052-4","article-title":"PPPLib: An open-source software for precise point positioning using GPS, BeiDou, Galileo, GLONASS, and QZSS with multi-frequency observations","volume":"25","author":"Chen","year":"2020","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1016\/j.asr.2020.12.022","article-title":"A variational Bayesian-based robust adaptive filtering for precise point positioning using undifferenced and uncombined observations","volume":"67","author":"Pan","year":"2021","journal-title":"Adv. Sp. Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Edokossi, K., Calabia, A., Jin, S., and Molina, I. (2020). GNSS-Reflectometry and remote sensing of soil moisture: A review of measurement techniques, methods, and applications. Remote Sens., 12.","DOI":"10.3390\/rs12040614"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Innerkofler, J., Kirchengast, G., Schw\u00e4rz, M., Pock, C., J\u00e4ggi, A., Andres, Y., and Marquardt, C. (2020). Precise orbit determination for Climate applications of GNSS radio occultation including uncertainty estimation. Remote Sens., 12.","DOI":"10.3390\/rs12071180"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/j.measurement.2011.12.021","article-title":"A new method of seamless land navigation for GPS\/INS integrated system","volume":"45","author":"Zhang","year":"2012","journal-title":"Measurement"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ma, L., You, Z., Liu, T., and Shi, S. (2016). Coupled integration of CSAC, MIMU, and GNSS for improved PNT performance. Sensors, 16.","DOI":"10.3390\/s16050682"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1017\/S0373463316000023","article-title":"Inertial aided cycle slip detection and repair for PPP\/INS tightly coupled navigation","volume":"69","author":"Li","year":"2016","journal-title":"J. Navig."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1109\/TVT.2012.2229306","article-title":"Low-cost antenna attitude estimation by fusing inertial sensing and two-antenna GPS for Vehicle-Mounted Satcom-on-the-Move","volume":"62","author":"Wu","year":"2013","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"1082","DOI":"10.3390\/mi6081082","article-title":"Quantitative analysis to the impacts of IMU quality in GPS\/INS deep integration","volume":"6","author":"Niu","year":"2015","journal-title":"Micromachines"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Reuper, B., Becker, M., and Leinen, S. (2018). Benefits of multi-constellation\/multi-frequency GNSS in a tightly coupled GNSS\/IMU\/odometry integration algorithm. Sensors, 18.","DOI":"10.3390\/s18093052"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1109\/TITS.2010.2052805","article-title":"Modeling the stochastic drift of a MEMS-based gyroscope in Gyro\/Odometer\/GPS integrated navigation","volume":"11","author":"Georgy","year":"2010","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TIM.2011.2159317","article-title":"Accurate pedestrian indoor navigation by tightly coupling foot-mounted IMU and RFID measurements","volume":"61","author":"Ruiz","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1017\/S0373463314000812","article-title":"Singular value decomposition-based robust cubature Kalman filtering for an integrated GPS\/SINS navigation system","volume":"68","author":"Zhang","year":"2015","journal-title":"J. Navig."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/LSP.2006.871854","article-title":"Neural network-aided adaptive unscented Kalman filter for nonlinear state estimation","volume":"13","author":"Zhan","year":"2006","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10291-007-0084-6","article-title":"Adaptive estimation of multiple fading factors in Kalman filter for navigation applications","volume":"12","author":"Geng","year":"2008","journal-title":"GPS Solut."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.1016\/j.automatica.2011.08.005","article-title":"Cubature Kalman smoothers","volume":"47","author":"Arasaratnam","year":"2011","journal-title":"Automatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109139","DOI":"10.1016\/j.measurement.2021.109139","article-title":"Multiple fading factors-based strong tracking variational bayesian adaptive Kalman filter","volume":"176","author":"Pan","year":"2021","journal-title":"Measurement"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/S1000-9361(11)60055-1","article-title":"Multiple fading factors Kalman filter for SINS static alignment application","volume":"24","author":"Gao","year":"2011","journal-title":"Chin. J. Aeronaut."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"105011","DOI":"10.1088\/0957-0233\/25\/10\/105011","article-title":"Adaptive robust Kalman filtering for precise point positioning","volume":"25","author":"Guo","year":"2014","journal-title":"Meas. Sci. Technol."},{"key":"ref_26","unstructured":"Shin, E.-H. (2005). Estimation Techniques for Low-Cost Inertial Navigation. [Ph.D. Thesis, University of Calgary]."},{"key":"ref_27","first-page":"58","article-title":"Application of robust adaptive EKF in INS\/GNSS tight combination","volume":"48","author":"Duan","year":"2019","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ma, C., Zhang, Q., Meng, X., Zheng, N., and Pan, S. (2020). A Novel ambiguity parameter estimation and elimination strategy for GNSS\/INS tightly coupled integration. Remote Sens., 12.","DOI":"10.3390\/rs12213514"},{"key":"ref_29","unstructured":"Zang, Z. (2015). Research of SINS\/GPS Tightly Integrated Navigation System Based on Pseudo-Range and Pseudo-Range Rate. [Master Thesis, Beijing Institute of Technology]. (In Chinese)."},{"key":"ref_30","first-page":"341","article-title":"Tightly GPS\/INS integrated navigation system based on single frequency pseudo-range and its rate","volume":"17","author":"Xie","year":"2017","journal-title":"Sci. Technol. Eng."},{"key":"ref_31","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. Automat. Contr."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2975","DOI":"10.1109\/TSP.2017.2679685","article-title":"Improved cubature Kalman filter for GNSS\/INS based on transformation of posterior sigma-points error","volume":"65","author":"Cui","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4176","DOI":"10.1109\/JSEN.2018.2820097","article-title":"An improved robust adaptive kalman filter for GNSS precise point positioning","volume":"18","author":"Zhang","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Huber, P.J. (1981). Robust Statistics, John Wiley & Sons.","DOI":"10.1002\/0471725250"},{"key":"ref_35","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"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/10\/1943\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:02:20Z","timestamp":1760162540000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/10\/1943"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,16]]},"references-count":35,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["rs13101943"],"URL":"https:\/\/doi.org\/10.3390\/rs13101943","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,16]]}}}