{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T17:11:55Z","timestamp":1774631515145,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T00:00:00Z","timestamp":1651190400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Regional Development Fund (ERDF)","award":["POCI-01-0247-FEDER-041435"],"award-info":[{"award-number":["POCI-01-0247-FEDER-041435"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The attitude and heading reference system (AHRS) is an important concept in the area of navigation, image stabilization, and object detection and tracking. Many studies and works have been conducted in this regard to estimate the accurate orientation of rigid bodies. In most research in this area, low-cost MEMS sensors are employed, but since the system\u2019s response will diverge over time due to integration drift, it is necessary to apply proper estimation algorithms. A two-step extended Kalman Filter (EKF) algorithm is used in this study to estimate the orientation of an IMU. A 9-DOF device is used for this purpose, including a 6-DOF IMU with a three-axis gyroscope and a three-axis accelerometer, and a three-axis magnetometer. In addition, to have an accurate algorithm, both IMU and magnetometer biases and disturbances are modeled and considered in the real-time filter. After applying the algorithm to the sensor\u2019s output, an accurate orientation as well as unbiased angular velocity, linear acceleration, and magnetic field were achieved. In order to demonstrate the reduction of noise power, fast Fourier transform (FFT) diagrams are used. The effect of the initial condition on the response of the system is also investigated.<\/jats:p>","DOI":"10.3390\/s22093416","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T07:08:58Z","timestamp":1651475338000},"page":"3416","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["9-DOF IMU-Based Attitude and Heading Estimation Using an Extended Kalman Filter with Bias Consideration"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7907-6216","authenticated-orcid":false,"given":"Sajjad Boorghan","family":"Farahan","sequence":"first","affiliation":[{"name":"Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1094-0114","authenticated-orcid":false,"given":"Jos\u00e9 J. M.","family":"Machado","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Mec\u00e2nica, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8573-967X","authenticated-orcid":false,"given":"Fernando Gomes","family":"de Almeida","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Mec\u00e2nica, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7603-6526","authenticated-orcid":false,"given":"Jo\u00e3o Manuel R. S.","family":"Tavares","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Mec\u00e2nica, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2852","DOI":"10.1109\/JSEN.2011.2170161","article-title":"A fully integrated inertial measurement unit: Application to attitude and heading determination","volume":"11","author":"Alandry","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kulakova, V.I., Markov, A.O., and Sokharev, A.Y. (2020, January 23\u201324). SINS\/GNSS Aided by Autonomous AHRS for a Small UAV. Proceedings of the 2020 European Navigation Conference (ENC), Online.","DOI":"10.23919\/ENC48637.2020.9317381"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Farhangian, F., and Landry, R. (2020). Accuracy improvement of attitude determination systems using EKF-based error prediction filter and PI controller. Sensors, 20.","DOI":"10.3390\/s20144055"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"9341","DOI":"10.1109\/JSEN.2021.3053843","article-title":"Attitude adaptive estimation with smartphone classification for pedestrian navigation","volume":"21","author":"Vertzberger","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ludwig, S.A. (2018, January 8\u201313). Genetic algorithm based Kalman filter adaptation algorithm for magnetic and inertial measurement unit. Proceedings of the 2018 IEEE Congress on Evolutionary Computation (CEC), Rio de Janeiro, Brazil.","DOI":"10.1109\/CEC.2018.8477940"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3561","DOI":"10.1109\/JSEN.2020.3026895","article-title":"Robust error-state Kalman filter for estimating IMU orientation","volume":"21","author":"Vitali","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bruschetta, M., Caiaffa, L., Picotti, E., and Beghi, A. (2021, January 22\u201325). Velocity Aided, Correlated Noise Extended Kalman Filtering for Attitude Estimation: A Motorcycle Case Study. Proceedings of the 2021 29th Mediterranean Conference on Control and Automation (MED), Online.","DOI":"10.1109\/MED51440.2021.9480325"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7082","DOI":"10.1109\/TIM.2020.2974135","article-title":"Adaptive attitude estimation for low-cost MEMS IMU using ellipsoidal method","volume":"69","author":"Park","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e1926","DOI":"10.1002\/stc.1926","article-title":"High-speed 6-DOF structural displacement monitoring by fusing ViSP (visually servoed paired structured light system) and IMU with extended Kalman filter","volume":"24","author":"Jeon","year":"2017","journal-title":"Struct. Control. Health Monit."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.sna.2007.05.008","article-title":"Calibration and data fusion solution for the miniature attitude and heading reference system","volume":"138","author":"Jurman","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Auysakul, J., Xu, H., and Pooneeth, V. (2018). A hybrid motion estimation for video stabilization based on an IMU sensor. Sensors, 18.","DOI":"10.3390\/s18082708"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"62","DOI":"10.5772\/58463","article-title":"A practical method for implementing an attitude and heading reference system","volume":"11","author":"Grau","year":"2014","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1017\/S037346330400270X","article-title":"Attitude estimation by separate-bias Kalman filter-based data fusion","volume":"57","author":"Setoodeh","year":"2004","journal-title":"J. Navig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1109\/LRA.2020.2968071","article-title":"Direct visual-inertial ego-motion estimation via iterated extended kalman filter","volume":"5","author":"Zhong","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1017\/S0373463312000331","article-title":"Effective adaptive Kalman filter for MEMS-IMU\/magnetometers integrated attitude and heading reference systems","volume":"66","author":"Li","year":"2013","journal-title":"J. Navig."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Deibe, \u00c1., Ant\u00f3n Nacimiento, J.A., Cardenal, J., and L\u00f3pez Pe\u00f1a, F. (2020). A Kalman Filter for nonlinear attitude estimation using time variable matrices and quaternions. Sensors, 20.","DOI":"10.3390\/s20236731"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3296","DOI":"10.1109\/TIM.2010.2047157","article-title":"Orientation estimation using a quaternion-based indirect Kalman filter with adaptive estimation of external acceleration","volume":"59","author":"Suh","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"148989","DOI":"10.1109\/ACCESS.2019.2946609","article-title":"Combined quaternion-based error state Kalman filtering and smooth variable structure filtering for robust attitude estimation","volume":"7","author":"Youn","year":"2019","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ko, N.Y., Choi, H.T., Lee, C.-M., and Moon, Y.S. (2016, January 10\u201313). Attitude estimation using depth measurement and AHRS data for underwater vehicle navigation. Proceedings of the OCEANS 2016, Shanghai, China.","DOI":"10.1109\/OCEANSAP.2016.7485508"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1109\/TNSRE.2005.847353","article-title":"Compensation of magnetic disturbances improves inertial and magnetic sensing of human body segment orientation","volume":"13","author":"Roetenberg","year":"2005","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Navidi, N., and Landry, R. (2021). A new perspective on low-cost mems-based AHRS determination. Sensors, 21.","DOI":"10.3390\/s21041383"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Fan, B., Li, Q., Wang, C., and Liu, T. (2017). An adaptive orientation estimation method for magnetic and inertial sensors in the presence of magnetic disturbances. Sensors, 17.","DOI":"10.3390\/s17051161"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.3390\/s130201919","article-title":"Extended Kalman filter-based methods for pose estimation using visual, inertial and magnetic sensors: Comparative analysis and performance evaluation","volume":"13","author":"Ligorio","year":"2013","journal-title":"Sensors"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Alatise, M.B., and Hancke, G.P. (2017). Pose estimation of a mobile robot based on fusion of IMU data and vision data using an extended Kalman filter. Sensors, 17.","DOI":"10.3390\/s17102164"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/s11071-021-07046-2","article-title":"Nonlinear dynamic analysis of a rotor-porous air journal bearing system with O-rings mounted","volume":"107","author":"Zhang","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1007\/s11071-016-3091-8","article-title":"Bifurcation in a planar four-bar mechanism with revolute clearance joint","volume":"87","author":"Farahan","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.apm.2019.03.026","article-title":"Nonlinear dynamic response of a spur gear pair based on the modeling of periodic mesh stiffness and static transmission error","volume":"72","author":"Yang","year":"2019","journal-title":"Appl. Math. Model."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.inffus.2021.04.009","article-title":"Sensor fusion algorithms for orientation tracking via magnetic and inertial measurement units: An experimental comparison survey","volume":"76","author":"Nazarahari","year":"2021","journal-title":"Inf. Fusion"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.inffus.2020.10.018","article-title":"40 years of sensor fusion for orientation tracking via magnetic and inertial measurement units: Methods, lessons learned, and future challenges","volume":"68","author":"Nazarahari","year":"2021","journal-title":"Inf. Fusion"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6771","DOI":"10.3390\/s110706771","article-title":"Data fusion algorithms for multiple inertial measurement units","volume":"11","author":"Bancroft","year":"2011","journal-title":"Sensors"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3133","DOI":"10.1109\/JIOT.2020.2965115","article-title":"Kalman-filter-based integration of IMU and UWB for high-accuracy indoor positioning and navigation","volume":"7","author":"Feng","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1850","DOI":"10.1109\/TMECH.2017.2698639","article-title":"Indirect Kalman filtering based attitude estimation for low-cost attitude and heading reference systems","volume":"22","author":"Chang","year":"2017","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1109\/JSEN.2019.2941273","article-title":"MEMS-based IMU drift minimization: Sage Husa adaptive robust Kalman filtering","volume":"20","author":"Narasimhappa","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Yan, Y., Cao, Y., Zhao, Z., and Li, D. (2019, January 22\u201324). An Adaptive Extended Kalman Filter for Non-Gravitational Acceleration Elimination in AHRS. Proceedings of the 2019 Chinese Automation Congress (CAC), Hangzhou, China.","DOI":"10.1109\/CAC48633.2019.8997337"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Benzerrouk, H., and Nebylov, A. (2018, January 28\u201330). Robust IMU\/UWB integration for indoor pedestrian navigation. Proceedings of the 2018 25th Saint Petersburg International Conference on Integrated Navigation Systems (ICINS), Saint Petersburg, Russia.","DOI":"10.23919\/ICINS.2018.8405844"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5653","DOI":"10.1109\/LRA.2020.3007421","article-title":"Tlio: Tight learned inertial odometry","volume":"5","author":"Liu","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"12369","DOI":"10.1109\/JSEN.2019.2940071","article-title":"Performance analysis of sensor fusion techniques for heading estimation using smartphone sensors","volume":"19","author":"Poulose","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_38","first-page":"1","article-title":"A Robust 6D Pose Tracking Approach by Fusing A Multi-Camera Tracking Device and An AHRS Module","volume":"71","author":"Wang","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3655","DOI":"10.1109\/JSEN.2019.2959574","article-title":"Neural network augmented sensor fusion for pose estimation of tensegrity manipulators","volume":"20","author":"Kuzdeuov","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5792","DOI":"10.1109\/LRA.2021.3085167","article-title":"Invariant Extended Kalman Filtering for Underwater Navigation","volume":"6","author":"Potokar","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_41","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":"2017","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10846-017-0522-9","article-title":"High precision stabilization of pan-tilt systems using reliable angular acceleration feedback from a master-slave Kalman filter","volume":"88","author":"Evren","year":"2017","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1109\/JSEN.2011.2166066","article-title":"Motion measurement using inertial sensors, ultrasonic sensors, and magnetometers with extended kalman filter for data fusion","volume":"12","author":"Zhao","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3299","DOI":"10.1109\/JSEN.2017.2787578","article-title":"Adaptive EKF based on HMM recognizer for attitude estimation using MEMS MARG sensors","volume":"18","author":"Tong","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Feng, K., Li, J., Zhang, X., Shen, C., Bi, Y., Zheng, T., and Liu, J. (2017). A new quaternion-based Kalman filter for real-time attitude estimation using the two-step geometrically-intuitive correction algorithm. Sensors, 17.","DOI":"10.3390\/s17092146"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"115101","DOI":"10.1088\/1361-6501\/aadc4c","article-title":"An orientation estimation algorithm based on multi-source information fusion","volume":"29","author":"Liu","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Fan, B., Li, Q., and Liu, T. (2018). How magnetic disturbance influences the attitude and heading in magnetic and inertial sensor-based orientation estimation. Sensors, 18.","DOI":"10.3390\/s18010076"},{"key":"ref_48","unstructured":"Farrell, J. (2008). Aided Navigation: GPS with High Rate Sensors, McGraw-Hill, Inc."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Kok, M., Hol, J.D., and Sch\u00f6n, T.B. (2017). Using inertial sensors for position and orientation estimation. arXiv.","DOI":"10.1561\/9781680833577"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1109\/TIM.2017.2761230","article-title":"Robust attitude estimation from uncertain observations of inertial sensors using covariance inflated multiplicative extended Kalman filter","volume":"67","author":"Ghobadi","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3416\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:04:21Z","timestamp":1760137461000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3416"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,29]]},"references-count":50,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["s22093416"],"URL":"https:\/\/doi.org\/10.3390\/s22093416","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,29]]}}}