{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T15:24:11Z","timestamp":1778426651067,"version":"3.51.4"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T00:00:00Z","timestamp":1645401600000},"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 inertial navigation system (INS) is a basic component to obtain a continuous navigation solution in various applications. The INS suffers from a growing error over time. In particular, its navigation solution depends mainly on the quality and grade of the inertial measurement unit (IMU), which provides the INS with both accelerations and angular rates. However, low-cost small micro-electro-mechanical systems (MEMSs) suffer from huge error sources such as bias, the scale factor, scale factor instability, and highly non-linear noise. Therefore, MEMS-IMU measurements lead to drifts in the solutions when used as a control input to the INS. Accordingly, several approaches have been introduced to model and mitigate the errors associated with the IMU. In this paper, a machine-learning-based adaptive neuro-fuzzy inference system (ML-based-ANFIS) is proposed to leverage the performance of low-grade IMUs in two phases. The first phase was training 50% of the low-grade IMU measurements with a high-end IMU to generate a suitable error model. The second phase involved testing the developed model on the remaining low-grade IMU measurements. A real road trajectory was used to evaluate the performance of the proposed algorithm. The results showed the effectiveness of utilizing the proposed ML-ANFIS algorithm to remove the errors and improve the INS solution compared to the traditional one. An improvement of 70% in the 2D positioning and of 92% in the 2D velocity of the INS solution were attained when the proposed algorithm was applied compared to the traditional INS solution.<\/jats:p>","DOI":"10.3390\/s22041687","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T20:48:41Z","timestamp":1645476521000},"page":"1687","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":50,"title":["A Machine Learning Approach for an Improved Inertial Navigation System Solution"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0621-3608","authenticated-orcid":false,"given":"Ahmed E.","family":"Mahdi","sequence":"first","affiliation":[{"name":"Electrical Engineering Branch, Military Technical College, Kobry El-Kobba, Cairo 11766, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7697-6611","authenticated-orcid":false,"given":"Ahmed","family":"Azouz","sequence":"additional","affiliation":[{"name":"Electrical Engineering Branch, Military Technical College, Kobry El-Kobba, Cairo 11766, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6702-4934","authenticated-orcid":false,"given":"Ahmed E.","family":"Abdalla","sequence":"additional","affiliation":[{"name":"Electrical Engineering Branch, Military Technical College, Kobry El-Kobba, Cairo 11766, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6319-2877","authenticated-orcid":false,"given":"Ashraf","family":"Abosekeen","sequence":"additional","affiliation":[{"name":"Electrical Engineering Branch, Military Technical College, Kobry El-Kobba, Cairo 11766, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Noureldin, A., Karamat, T.B., and Georgy, J. (2013). Fundamentals of Inertial Navigation, Satellite-Based Positioning and their Integration, Springer.","DOI":"10.1007\/978-3-642-30466-8"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Titterton, D., and Weston, J. (2004). Strapdown Inertial Navigation Technology, Institution of Engineering and Technology.","DOI":"10.1049\/PBRA017E"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4838","DOI":"10.1109\/TITS.2020.2980307","article-title":"A Novel Multi-Level Integrated Navigation System for Challenging GNSS Environments","volume":"22","author":"Abosekeen","year":"2021","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_4","unstructured":"Li, Y., Chen, R., Niu, X., Zhuang, Y., Gao, Z., Hu, X., and El-Sheimy, N. (2020). Inertial Sensing Meets Artificial Intelligence: Opportunity or Challenge?. arXiv."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Abosekeen, A., Noureldin, A., Karamat, T., and Korenberg, M.J. (2017, January 25\u201329). Comparative Analysis of Magnetic-Based RISS using Different MEMS-Based Sensors. Proceedings of the 30th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2017), Portland, OR, USA.","DOI":"10.33012\/2017.15120"},{"key":"ref_6","first-page":"36","article-title":"Improved Navigation Through GNSS Outages: Fusing Automotive Radar and OBD-II Speed Measurements with Fuzzy Logic","volume":"32","author":"Abosekeen","year":"2021","journal-title":"GPS World"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Nam, D.V., and Gon-Woo, K. (2020). Robust Stereo Visual Inertial Navigation System Based on Multi-Stage Outlier Removal in Dynamic Environments. Sensors, 20.","DOI":"10.3390\/s20102922"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Abosekeen, A., Iqbal, U., and Noureldin, A. (2020, January 21\u201325). Enhanced Land Vehicles Navigation by Fusing Automotive Radar and Speedometer Data. Proceedings of the 33rd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2020), St. Louise, MO, USA.","DOI":"10.33012\/2020.17527"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Abosekeen, A., and Abdalla, A. (2012, January 29\u201331). Fusion of Low-Cost MEMS IMU\/GPS Integrated Navigation System. Proceedings of the 8th International Conference on Electrical Engineering, Cairo, Egypt.","DOI":"10.21608\/iceeng.2012.30810"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Rashed, M.A., Abosekeen, A., Ragab, H., Noureldin, A., and Korenberg, M.J. (2019, January 16\u201320). Leveraging FMCW-radar for autonomous positioning systems: Methodology and application in downtown Toronto. Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019, Miami, FL, USA.","DOI":"10.33012\/2019.17096"},{"key":"ref_11","unstructured":"Hsu, L.T. (2020). What are the roles of artificial intelligence and machine learning in GNSS positioning?. Inside GNSS, 1\u20138."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/MAES.2005.1412121","article-title":"Online INS\/GPS Integration with a Radial Basis Function Neural Network","volume":"20","author":"Sharaf","year":"2005","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2783","DOI":"10.1088\/0957-0233\/17\/10\/033","article-title":"Bridging GPS outages using neural network estimates of INS position and velocity errors","volume":"17","author":"Semeniuk","year":"2006","journal-title":"Meas. Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/TNN.2006.890811","article-title":"Sensor Integration for Satellite-Based Vehicular Navigation Using Neural Networks","volume":"18","author":"Sharaf","year":"2007","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_15","first-page":"140","article-title":"Performance evaluation of neural-network-based integration of vision and motion sensors for vehicular navigation","volume":"Volume 11009","author":"Dudzik","year":"2019","journal-title":"Autonomous Systems: Sensors, Processing, and Security for Vehicles and Infrastructure 2019"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Jaradat, M.A., Abdel-Hafez, M.F., Saadeddin, K., and Jarrah, M.A. (2013, January 9\u201311). Intelligent fault detection and fusion for INS\/GPS navigation system. Proceedings of the 2013 9th International Symposium on Mechatronics and its Applications (ISMA), Amman, Jordan.","DOI":"10.1109\/ISMA.2013.6547398"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2021\/4862451","article-title":"The Integration of Rotary MEMS INS and GNSS with Artificial Neural Networks","volume":"2021","author":"Du","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"108391","DOI":"10.1016\/j.measurement.2020.108391","article-title":"A new method for compensating the errors of integrated navigation systems using artificial neural networks","volume":"168","author":"Gavrilov","year":"2021","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tamazin, M., Korenberg, M.J., Elghamrawy, H., and Noureldin, A. (2021). GPS Swept Anti-Jamming Technique Based on Fast Orthogonal Search (FOS). Sensors, 21.","DOI":"10.3390\/s21113706"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Iqbal, U., Abosekeen, A., Georgy, J., Umar, A., Noureldin, A., and Korenberg, M.J. (2021). Implementation of Parallel Cascade Identification at Various Phases for Integrated Navigation System. Future Internet, 13.","DOI":"10.3390\/fi13080191"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"S\u00e1nchez Morales, E., Dauth, J., Huber, B., Garc\u00eda Higuera, A., and Botsch, M. (2021). High Precision Outdoor and Indoor Reference State Estimation for Testing Autonomous Vehicles. Sensors, 21.","DOI":"10.3390\/s21041131"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Semanjski, S., Semanjski, I., De Wilde, W., and Muls, A. (2020). Use of Supervised Machine Learning for GNSS Signal Spoofing Detection with Validation on Real-World Meaconing and Spoofing Data\u2014Part I. Sensors, 20.","DOI":"10.3390\/s20041171"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1049\/rsn2.12144","article-title":"INS\/GPS Sensor Fusion based on Adaptive Fuzzy EKF with Sensitivity to Disturbances","volume":"15","author":"Sabzevari","year":"2021","journal-title":"IET Radar Sonar Navig."},{"key":"ref_24","first-page":"1","article-title":"Improving the Navigation System of a UAV Using Multi-Sensor Data Fusion Based on Fuzzy C-Means Clustering","volume":"14","author":"Abosekeen","year":"2011","journal-title":"Int. Conf. Aerosp. Sci. Aviat. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"95180","DOI":"10.1109\/ACCESS.2021.3094120","article-title":"A Temperature Compensation Approach for Dual-Mass MEMS Gyroscope Based on PE-LCD and ANFIS","volume":"9","author":"Cao","year":"2021","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Duan, Y., Li, H., Wu, S., and Zhang, K. (2021). INS Error Estimation Based on an ANFIS and Its Application in Complex and Covert Surroundings. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10060388"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/3145436","article-title":"TLBO-Based Adaptive Neurofuzzy Controller for Mobile Robot Navigation in a Strange Environment","volume":"2018","author":"Aouf","year":"2018","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"61296","DOI":"10.1109\/ACCESS.2019.2911025","article-title":"A Fusion Methodology to Bridge GPS Outages for INS\/GPS Integrated Navigation System","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"44087","DOI":"10.1109\/ACCESS.2020.2977474","article-title":"A Robust Fusion Methodology for MEMS-Based Land Vehicle Navigation in GNSS-Challenged Environments","volume":"8","author":"Yue","year":"2020","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"13714","DOI":"10.1109\/JSEN.2021.3053260","article-title":"Online Self-Calibration of Multiple 2D LiDARs Using Line Features with Fuzzy Adaptive Covariance","volume":"21","author":"Nam","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, Y., Chen, R., Niu, X., Zhuang, Y., Gao, Z., Hu, X., and El-Sheimy, N. (2021). Inertial Sensing Meets Machine Learning: Opportunity or Challenge?. IEEE Trans. Intell. Transp. Syst., 1\u201317.","DOI":"10.1109\/TITS.2021.3113995"},{"key":"ref_32","unstructured":"Groves, P.D. (2008). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House. [2nd ed.]."},{"key":"ref_33","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_34","unstructured":"Abosekeen, A. (2012). Multi-Sensor Integration and Fusion in Navigation Systems. [Master\u2019s Thesis, Military Technical College]."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1177\/0278364907079279","article-title":"An Introduction to Inertial and Visual Sensing","volume":"26","author":"Corke","year":"2007","journal-title":"Int. J. Robot. Res."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Huang, G. (2019, January 20\u201324). Visual-Inertial Navigation: A Concise Review. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8793604"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1250","DOI":"10.1109\/TITS.2019.2905871","article-title":"Improving the RISS\/GNSS Land-Vehicles Integrated Navigation System Using Magnetic Azimuth Updates","volume":"21","author":"Abosekeen","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_38","first-page":"1","article-title":"Representing attitude: Euler angles, unit quaternions, and rotation vectors","volume":"58","author":"Diebel","year":"2006","journal-title":"Matrix"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/917147","article-title":"Performance analysis of adaptive neuro fuzzy inference system control for mems navigation system","volume":"2014","author":"Zhang","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1109\/TLT.2011.36","article-title":"Modeling and Simulation of an Adaptive Neuro-Fuzzy Inference System (ANFIS) for Mobile Learning","volume":"5","author":"Shen","year":"2012","journal-title":"IEEE Trans. Learn. Technol."},{"key":"ref_41","unstructured":"Khan, M.A., and Ansari, A.Q. (2012). Fuzzy Logic: Concepts, System Design, and Applications to Industrial Informatics. Handbook of Research on Industrial Informatics and Manufacturing Intelligence: Innovations and Solutions, IGI Global. Chapter 3."},{"key":"ref_42","first-page":"2803","article-title":"Design of ANFIS based Estimation and Control for MIMO Systems","volume":"2","author":"Sivakumar","year":"2012","journal-title":"Int. J. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"9752","DOI":"10.1016\/j.eswa.2011.02.024","article-title":"Application of Neuro-Fuzzy Controller for Sumo Robot control","volume":"38","author":"Erdem","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/21.256541","article-title":"ANFIS: Adaptive-network-based fuzzy inference system","volume":"23","author":"Jang","year":"1993","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_45","unstructured":"Jin, Z., and Bose, B. (2002, January 5\u20138). Evaluation of membership functions for fuzzy logic controlled induction motor drive. Proceedings of the IEEE 2002 28th Annual Conference of the Industrial Electronics Society. IECON 02, Seville, Spain."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Prajapati, S., and Fernandez, E. (2020, January 2\u20134). Performance Evaluation of Membership Function on Fuzzy Logic Model for Solar PV array. Proceedings of the 2020 IEEE International Conference on Computing, Power and Communication Technologies (GUCON), Greater Noida, India.","DOI":"10.1109\/GUCON48875.2020.9231202"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/4\/1687\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:24:13Z","timestamp":1760135053000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/4\/1687"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,21]]},"references-count":46,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["s22041687"],"URL":"https:\/\/doi.org\/10.3390\/s22041687","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202202.0193.v1","asserted-by":"object"}]},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,21]]}}}