{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T17:37:01Z","timestamp":1786210621260,"version":"3.56.0"},"reference-count":68,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,6]],"date-time":"2021-02-06T00:00:00Z","timestamp":1612569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Kalman filter variants extended Kalman filter (EKF) and error-state Kalman filter (ESKF) are widely used in underwater multi-sensor fusion applications for localization and navigation. Since these filters are designed by employing first-order Taylor series approximation in the error covariance matrix, they result in a decrease in estimation accuracy under high nonlinearity. In order to address this problem, we proposed a novel multi-sensor fusion algorithm for underwater vehicle localization that improves state estimation by augmentation of the radial basis function (RBF) neural network with ESKF. In the proposed algorithm, the RBF neural network is utilized to compensate the lack of ESKF performance by improving the innovation error term. The weights and centers of the RBF neural network are designed by minimizing the estimation mean square error (MSE) using the steepest descent optimization approach. To test the performance, the proposed RBF-augmented ESKF multi-sensor fusion was compared with the conventional ESKF under three different realistic scenarios using Monte Carlo simulations. We found that our proposed method provides better navigation and localization results despite high nonlinearity, modeling uncertainty, and external disturbances.<\/jats:p>","DOI":"10.3390\/s21041149","type":"journal-article","created":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T04:33:46Z","timestamp":1612931626000},"page":"1149","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":95,"title":["Multi-Sensor Fusion for Underwater Vehicle Localization by Augmentation of RBF Neural Network and Error-State Kalman Filter"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8363-349X","authenticated-orcid":false,"given":"Nabil","family":"Shaukat","sequence":"first","affiliation":[{"name":"Oceanic Engineering Research Institute, University of Malaga, 29010 Malaga, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9848-8598","authenticated-orcid":false,"given":"Ahmed","family":"Ali","sequence":"additional","affiliation":[{"name":"Oceanic Engineering Research Institute, University of Malaga, 29010 Malaga, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Javed Iqbal","sequence":"additional","affiliation":[{"name":"Oceanic Engineering Research Institute, University of Malaga, 29010 Malaga, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4735-0692","authenticated-orcid":false,"given":"Muhammad","family":"Moinuddin","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Center of Excellence in Intelligent Engineering Systems, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3042-4392","authenticated-orcid":false,"given":"Pablo","family":"Otero","sequence":"additional","affiliation":[{"name":"Oceanic Engineering Research Institute, University of Malaga, 29010 Malaga, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106146","DOI":"10.1016\/j.oceaneng.2019.106146","article-title":"A novel self-adapting filter based navigation algorithm for autonomous underwater vehicles","volume":"187","author":"Xu","year":"2019","journal-title":"Ocean Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Allotta, B., Chisci, L., Costanzi, R., Fanelli, F., Fantacci, C., Meli, E., Ridolfi, A., Caiti, A., Di Corato, F., and Fenucci, D. (2015, January 18\u201321). A comparison between EKF-based and UKF-based navigation algorithms for AUVs localization. Proceedings of the OCEANS 2015\u2014Genova, Genoa, Italy.","DOI":"10.1109\/OCEANS-Genova.2015.7271681"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2683","DOI":"10.1109\/TCYB.2015.2484378","article-title":"A Fast Adaptive Tunable RBF Network For Nonstationary Systems","volume":"46","author":"Chen","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Tomczyk, K., Piekarczyk, M., and Sokal, G. (2019). Radial basis functions intended to determine the upper bound of absolute dynamic error at the output of voltage-mode accelerometers. Sensors, 19.","DOI":"10.3390\/s19194154"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1109\/72.668883","article-title":"Robust nonlinear system identification using neural-network models","volume":"9","author":"Lu","year":"1998","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_6","unstructured":"Li, D.M., and Li, F.C. (2009, January 12\u201315). Identification of chaotic systems with noisy data based on RBF neural networks. Proceedings of the 2009 International Conference on Machine Learning and Cybernetics, Hebei, China."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1109\/MAES.2014.130191","article-title":"Navigation using inertial sensors [Tutorial]","volume":"30","author":"Groves","year":"2015","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1109\/JOE.2018.2832878","article-title":"A Navigation Solution Using a MEMS IMU, Model-Based Dead-Reckoning, and One-Way-Travel-Time Acoustic Range Measurements for Autonomous Underwater Vehicles","volume":"44","author":"Kepper","year":"2019","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.oceaneng.2017.04.047","article-title":"Survey on advances on terrain based navigation for autonomous underwater vehicles","volume":"139","author":"Melo","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez-Garc\u00eda, J., G\u00f3mez-Espinosa, A., Cuan-Urquizo, E., Garc\u00eda-Valdovinos, L.G., Salgado-Jim\u00e9nez, T., and Escobedo Cabello, J.A. (2020). Autonomous underwater vehicles: Localization, navigation, and communication for collaborative missions. Appl. Sci., 10.","DOI":"10.3390\/app10041256"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"45693","DOI":"10.1109\/ACCESS.2019.2909133","article-title":"Localization and Detection of Targets in Underwater Wireless Sensor Using Distance and Angle Based Algorithms","volume":"7","author":"Ullah","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/JOE.2013.2278891","article-title":"AUV Navigation and Localization: A Review","volume":"39","author":"Paull","year":"2014","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Qureshi, U.M., Aziz, Z., Shaikh, F.K., Aziz, Z., Shah, S.M.S., Shah, S.M.S., Sheikh, A.A., Felemban, E., and Qaisar, S.B. (2016). RF path and absorption loss estimation for underwaterwireless sensor networks in differentwater environments. Sensors, 16.","DOI":"10.3390\/s16060890"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.1109\/TAC.2005.854627","article-title":"Kalman filtering in extended noise environments","volume":"50","author":"Diversi","year":"2005","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Almeida, J., Matias, B., Ferreira, A., Almeida, C., Martins, A., and Silva, E. (2020). Underwater localization system combining iusbl with dynamic sbl in \u00a1vamos! trials. Sensors, 20.","DOI":"10.3390\/s20174710"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ko, N.Y., Jeong, S., Hwang, S.S., and Pyun, J.Y. (2019). Attitude estimation of underwater vehicles using field measurements and bias compensation. Sensors, 19.","DOI":"10.3390\/s19020330"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"23041","DOI":"10.3390\/s141223041","article-title":"Study of the algorithm of backtracking decoupling and adaptive extended kalman filter based on the quaternion expanded to the state variable for underwater glider navigation","volume":"14","author":"Huang","year":"2014","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Miller, A., Miller, B., and Miller, G. (2019). On AUV control with the aid of position estimation algorithms based on acoustic seabed sensing and DOA measurements. Sensors, 19.","DOI":"10.3390\/s19245520"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tal, A., Klein, I., and Katz, R. (2017). Inertial navigation system\/doppler velocity log (INS\/DVL) fusion with partial dvl measurements. Sensors, 17.","DOI":"10.3390\/s17020415"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhang, M., Li, K., Hu, B., and Meng, C. (2019). Comparison of Kalman Filters for Inertial Integrated Navigation. Sensors, 19.","DOI":"10.3390\/s19061426"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sun, C., Zhang, Y., Wang, G., and Gao, W. (2018). A new variational bayesian adaptive extended kalman filter for cooperative navigation. Sensors, 18.","DOI":"10.3390\/s18082538"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1656","DOI":"10.1109\/TIM.2013.2292277","article-title":"A Hybrid Prediction Method for Bridging GPS Outages in High-Precision POS Application","volume":"63","author":"Chen","year":"2014","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jingsen, Z., Wenjie, Z., Bo, H., and Yali, W. (2016, January 8\u201310). Integrating Extreme Learning Machine with Kalman Filter to Bridge GPS Outages. Proceedings of the 2016 3rd International Conference on Information Science and Control Engineering, ICISCE 2016, Beijing, China.","DOI":"10.1109\/ICISCE.2016.98"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s11036-017-0962-2","article-title":"Editorial: Machine Learning and Intelligent Communications","volume":"23","author":"Huang","year":"2018","journal-title":"Mob. Netw. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.adhoc.2017.09.003","article-title":"Interest-aware energy collection & resource management in machine to machine communications","volume":"68","author":"Tsiropoulou","year":"2018","journal-title":"Ad Hoc Netw."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, X., Mu, X., Liu, H., He, B., and Yan, T. (2019, January 16\u201319). Application of Modified EKF Based on Intelligent Data Fusion in AUV Navigation. Proceedings of the 2019 IEEE Underwater Technology (UT), Kaohsiung, Taiwan.","DOI":"10.1109\/UT.2019.8734414"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/JOE.2017.2769838","article-title":"A Low-Cost Dead Reckoning Navigation System for an AUV Using a Robust AHRS: Design and Experimental Analysis","volume":"43","author":"Sabet","year":"2018","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.mechatronics.2016.05.007","article-title":"An unscented Kalman filter based navigation algorithm for autonomous underwater vehicles","volume":"39","author":"Allotta","year":"2016","journal-title":"Mechatronics"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/9.847726","article-title":"A new method for the nonlinear transformation of means and covariances in filters and estimators","volume":"45","author":"Julier","year":"2000","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Karimi, M., Bozorg, M., and Khayatian, A.R. (2013, January 13\u201315). A comparison of DVL\/INS fusion by UKF and EKF to localize an autonomous underwater vehicle. Proceedings of the 2013 First RSI\/ISM International Conference on Robotics and Mechatronics (ICRoM), Tehran, Iran.","DOI":"10.1109\/ICRoM.2013.6510082"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4869","DOI":"10.1109\/TAC.2017.2694350","article-title":"SVD-Based Kalman Filter Derivative Computation","volume":"62","author":"Tsyganova","year":"2017","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Huang, G., Mourikis, A., and Roumeliotis, S. (2009, January 12\u201317). On the complexity and consistency of UKF-based SLAM. Proceedings of the 2009 IEEE International Conference on Robotics and Automation, Kobe, Japan.","DOI":"10.1109\/ROBOT.2009.5152793"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/S0925-2312(01)00611-7","article-title":"Training radial basis neural networks with the extended Kalman filter","volume":"48","author":"Simon","year":"2002","journal-title":"Neurocomputing"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.ijnaoe.2019.11.004","article-title":"Experimental and numerical study of autopilot using Extended Kalman Filter trained neural networks for surface vessels","volume":"12","author":"Wang","year":"2020","journal-title":"Int. J. Nav. Archit. Ocean."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6312","DOI":"10.3390\/s90806312","article-title":"A Comparison of RBF Neural Network Training Algorithms for Inertial Sensor Based Terrain Classification","volume":"9","author":"Kurban","year":"2009","journal-title":"Sensors"},{"key":"ref_36","unstructured":"Dong, X., Wu, J., Wang, S., and Chen, T. (2012, January 9\u201311). An improved CDKF algorithm based on RBF neural network for satellite attitude determination. Proceedings of the 2012 International Conference on Image Analysis and Signal Processing, IASP 2012, Huangzhou, China."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"105527","DOI":"10.1016\/j.ast.2019.105527","article-title":"Radial basis function neural network aided adaptive extended Kalman filter for spacecraft relative navigation","volume":"96","author":"Pesce","year":"2020","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1109\/72.392252","article-title":"Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks","volume":"6","author":"Chen","year":"1995","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s40092-016-0146-x","article-title":"On the use of back propagation and radial basis function neural networks in surface roughness prediction","volume":"12","author":"Markopoulos","year":"2016","journal-title":"J. Ind. Eng. Int."},{"key":"ref_40","unstructured":"Farrell, J.A. (2008). Aided Navigation GPS with High Rate Sensors, The McGraw-Hill Companies. [1st ed.]."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"208","DOI":"10.2514\/2.4242","article-title":"Strapdown Inertial Navigation Integration Algorithm Design Part 2: Velocity and Position Algorithms","volume":"21","author":"Savage","year":"1998","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/JOE.2010.2052691","article-title":"Autonomous Underwater Vehicle Navigation","volume":"35","author":"Miller","year":"2010","journal-title":"IEEE J. Ocean Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1002\/navi.271","article-title":"Design and practical implementation of kinematic constraints in Inertial Navigation System-Doppler Velocity Log (INS-DVL)-based navigation","volume":"65","author":"Karmozdi","year":"2018","journal-title":"Navigation"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Titterton, D., and Weston, J. (2004). Strapdown Inertial Navigation Technology, Institution of Engineering and Technology, The Institution of Engineering and Technology, Michael Faraday House. [2nd ed.].","DOI":"10.1049\/PBRA017E"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"19302","DOI":"10.3390\/s150819302","article-title":"Keeping a good attitude: A quaternion-based orientation filter for IMUs and MARGs","volume":"15","author":"Valenti","year":"2015","journal-title":"Sensors"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Grewal, M.S., Andrews, A.P., and Bartone, C.G. (2020). Global Navigation Satellite Systems, Inertial Navigation, and Integration, Wiley.","DOI":"10.1002\/9781119547860"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Chatfield, A.B. (1997). Fundamentals Of High Accuracy Inertial Navigation, American Institute of Aeronautics and Astronautics.","DOI":"10.2514\/4.866463"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Wang, Q., Cui, X., Li, Y., and Ye, F. (2017). Performance enhancement of a USV INS\/CNS\/DVL integration navigation system based on an adaptive information sharing factor federated filter. Sensor, 17.","DOI":"10.3390\/s17020239"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"He, K., Liu, H., and Wang, Z. (2020). A novel adaptive two-stage information filter approach for deep-sea USBL\/DVL integrated navigation. Sensors, 20.","DOI":"10.3390\/s20216029"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Hegrenaes, O., Ramstad, A., Pedersen, T., and Velasco, D. (2016, January 6\u20139). Validation of a new generation DVL for underwater vehicle navigation. Proceedings of the 2016 IEEE\/OES Autonomous Underwater Vehicles (AUV), Tokyo, Japan.","DOI":"10.1109\/AUV.2016.7778694"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Kang, Y., Zhao, L., Cheng, J., Wu, M., and Fan, X. (2018). A Novel Grid SINS\/DVL Integrated Navigation Algorithm for Marine Application. Sensors, 18.","DOI":"10.3390\/s18020364"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Christ, R.D., and Wernli, R.L. (2007). Underwater Acoustics and Positioning. The ROV Manual, Elsevier Ltd.","DOI":"10.1016\/B978-075068148-3\/50008-6"},{"key":"ref_53","unstructured":"Healey, A., An, E., and Marco, D. (1998, January 21). Online compensation of heading sensor bias for low cost AUVs. Proceedings of the 1998 Workshop on Autonomous Underwater Vehicles (Cat. No.98CH36290), Cambridge, MA, USA."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Fanelli, F. (2020). Development and Testing of Navigation Algorithms for Autonomous Underwater Vehicles, Springer International Publishing. [1st ed.]. Springer Theses.","DOI":"10.1007\/978-3-030-15596-4"},{"key":"ref_55","unstructured":"Roumeliotis, S.I., Sukhatme, G.S., and Bekey, G.A. (1999, January 10\u201315). Circumventing Dynamic Modeling: Evaluation of the Error-State Kalman Filter applied to Mobile Robot Localization. Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, MI, USA."},{"key":"ref_56","unstructured":"Rogers, R.M. (2007). Applied Mathematics in Integrated Navigation Systems, American Institute of Aeronautics and Astronautics. [3rd ed.]."},{"key":"ref_57","unstructured":"Foss, H.T.H., and Meland, E. (2007). Sensor Integration for Nonlinear Navigation System in Underwater Vehicles. [Ph.D. Thesis, Norwegian University of Science and Technology]."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1161","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_59","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1080\/20464177.2015.1022382","article-title":"Integration of navigation systems for autonomous underwater vehicles","volume":"14","author":"Dinc","year":"2015","journal-title":"J. Mar. Eng. Technol."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"5438","DOI":"10.1109\/TIE.2011.2164773","article-title":"Advantages of Radial Basis Function Networks for Dynamic System Design","volume":"58","author":"Yu","year":"2011","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5402\/2012\/324194","article-title":"Using Radial Basis Function Networks for Function Approximation and Classification","volume":"2012","author":"Wu","year":"2012","journal-title":"ISRN Appl. Math."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A New Approach to Linear Filtering and Prediction Problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_63","unstructured":"Sol\u00e0, J. (2017). Quaternion kinematics for the error-state Kalman filter. arXiv."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"3682","DOI":"10.1007\/s00034-019-01031-2","article-title":"A State-Space Backpropagation Algorithm for Nonlinear Estimation","volume":"38","author":"Bjaili","year":"2019","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Wang, D., and Wang, L. (2019). Convolution Accelerator Designs Using Fast Algorithms. Algorithms, 12.","DOI":"10.3390\/a12050112"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Dul, F., Lichota, P., and Rusowicz, A. (2020). Generalized Linear Quadratic Control for a Full Tracking Problem in Aviation. Sensors, 20.","DOI":"10.3390\/s20102955"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.1109\/TIM.2013.2265476","article-title":"Camera\/Laser\/GPS Fusion Method for Vehicle Positioning Under Extended NIS-Based Sensor Validation","volume":"62","author":"Wei","year":"2013","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1109\/TAES.2014.130204","article-title":"Gain-scheduled extended kalman filter for nanosatellite attitude determination system","volume":"51","author":"Pham","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/4\/1149\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:20:39Z","timestamp":1760160039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/4\/1149"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,6]]},"references-count":68,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["s21041149"],"URL":"https:\/\/doi.org\/10.3390\/s21041149","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,6]]}}}