{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:10:54Z","timestamp":1770898254141,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2013,2,4]],"date-time":"2013-02-04T00:00:00Z","timestamp":1359936000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper measurements from a monocular vision system are fused with inertial\/magnetic measurements from an Inertial Measurement Unit (IMU) rigidly connected to the camera. Two Extended Kalman filters (EKFs) were developed to estimate the pose of the IMU\/camera sensor moving relative to a rigid scene (ego-motion), based on a set of fiducials. The two filters were identical as for the state equation and the measurement equations of the inertial\/magnetic sensors. The DLT-based EKF exploited visual estimates of the ego-motion using a variant of the Direct Linear Transformation (DLT) method;  the error-driven EKF exploited pseudo-measurements based on the projection errors from measured two-dimensional point features to the corresponding three-dimensional fiducials. The two filters were off-line analyzed in different experimental conditions and compared to a purely IMU-based EKF used for estimating the orientation of the IMU\/camera sensor. The DLT-based EKF was more accurate than the error-driven EKF, less robust against loss of visual features, and equivalent in terms of computational complexity. Orientation root mean square errors (RMSEs) of 1\u00b0 (1.5\u00b0), and position RMSEs of 3.5 mm (10 mm) were achieved in our experiments by the DLT-based EKF (error-driven EKF); by contrast, orientation RMSEs of 1.6\u00b0 were achieved by the purely IMU-based EKF.<\/jats:p>","DOI":"10.3390\/s130201919","type":"journal-article","created":{"date-parts":[[2013,2,4]],"date-time":"2013-02-04T11:10:35Z","timestamp":1359976235000},"page":"1919-1941","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":80,"title":["Extended Kalman Filter-Based Methods for Pose  Estimation Using Visual, Inertial and Magnetic Sensors:  Comparative Analysis and Performance Evaluation"],"prefix":"10.3390","volume":"13","author":[{"given":"Gabriele","family":"Ligorio","sequence":"first","affiliation":[{"name":"The Institute of BioRobotics, Scuola Superiore Sant'Anna, Piazza Martiri della Libert\u00e0 33, 56124 Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3306-6498","authenticated-orcid":false,"given":"Angelo","family":"Sabatini","sequence":"additional","affiliation":[{"name":"The Institute of BioRobotics, Scuola Superiore Sant'Anna, Piazza Martiri della Libert\u00e0 33, 56124 Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MCG.2002.1046626","article-title":"Motion tracking: No silver bullet, but a respectable arsenal","volume":"22","author":"Welch","year":"2002","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s11554-007-0040-2","article-title":"Robust real-time tracking by fusing measurements from inertial and vision sensors","volume":"2","author":"Hol","year":"2007","journal-title":"J. Real-Time Imag. Proc."},{"key":"ref_3","unstructured":"Bleser, G., Hendeby, G., and Miezal, M. (October, January 26\u2013). Using Egocentric Vision to Achieve Robust Inertial Body Tracking under Magnetic Disturbances. Basel, Switzerland."},{"key":"ref_4","unstructured":"Vieville, T., Romann, F., Hotz, B., Mathieu, H., Buffa, M., Robert, L., Facao, P.E.D.S., Faugeras, O.D., and Audren, J.T. Autonomous Navigation of a Mobile Robot Using Inertial and Visual Cues. 26\u201330 July 1993."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1177\/0278364910382802","article-title":"Visual-inertial sensor fusion: Localization, mapping and sensor-to-sensor self-calibration","volume":"30","author":"Kelly","year":"2011","journal-title":"Int. J. Robot. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s10846-010-9490-z","article-title":"Fusion of IMU and vision for absolute scale estimation in monocular Slam","volume":"61","author":"Weiss","year":"2011","journal-title":"J. Intell. Robot Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Achtelik, M., Weiss, S., and Siegwart, R. (2011, January 9\u201313). Onboard IMU and Monocular Vision Based Control for MAVs in Unknown in- and Outdoor Environments. Shangai, China.","DOI":"10.1109\/ICRA.2011.5980343"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1177\/0278364907079278","article-title":"Integration of vision and inertial sensors for 3D arm motion tracking in home-based rehabilitation","volume":"26","author":"Tao","year":"2007","journal-title":"Int. J. Rob. Res."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hartley, R., and Zisserman, A. (2003). Multiple View Geometry in Computer Vision, Cambridge University Press.","DOI":"10.1017\/CBO9780511811685"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.3390\/s110201489","article-title":"Estimating three-dimensional orientation of human body parts by inertial\/magnetic sensing","volume":"11","author":"Sabatini","year":"2011","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/MCG.2005.140","article-title":"Pedestrian tracking with shoe-mounted inertial sensors","volume":"25","author":"Foxlin","year":"2005","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3018","DOI":"10.1109\/TIM.2010.2046595","article-title":"Personal navigation via high-resolution gait-corrected inertial measurement units","volume":"59","author":"Bebek","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_13","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. Rob. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1002\/cav.161","article-title":"Use of inertial sensors to support video tracking: Research articles","volume":"18","author":"Aron","year":"2007","journal-title":"Comput. Animat. Virt. World."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1016\/j.imavis.2004.02.007","article-title":"Tightly integrated sensor fusion for robust visual tracking","volume":"22","author":"Klein","year":"2004","journal-title":"Imag. Vis. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1755","DOI":"10.1177\/0278364911416391","article-title":"Gyro-aided feature tracking for a moving camera: Fusion, auto-calibration and gpu implementation","volume":"30","author":"Hwangbo","year":"2011","journal-title":"Int. J. Robot. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2982","DOI":"10.1364\/JOSAA.18.002982","article-title":"Robust structure from motion estimation using inertial data","volume":"18","author":"Qian","year":"2001","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1177\/0278364907080058","article-title":"Simultaneous motion and structure estimation by fusion of inertial and vision data","volume":"26","author":"Gemeiner","year":"2007","journal-title":"Int. J. Robot. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1109\/TBME.2006.875664","article-title":"Quaternion-based extended kalman filter for determining orientation by inertial and magnetic sensing","volume":"53","author":"Sabatini","year":"2006","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1109\/TRO.2006.886270","article-title":"Design, implementation, and experimental results of a quaternion-based kalman filter for human body motion tracking","volume":"22","author":"Yun","year":"2006","journal-title":"IEEE Trans. Robot."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1109\/TBME.2006.889184","article-title":"Ambulatory position and orientation tracking fusing magnetic and inertial sensing","volume":"54","author":"Roetenberg","year":"2007","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_22","first-page":"439","article-title":"Survey of attitude representations","volume":"41","author":"Shuster","year":"1993","journal-title":"J. Astronaut. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1177\/0278364907079276","article-title":"Relative pose calibration between visual and inertial sensors","volume":"26","author":"Lobo","year":"2007","journal-title":"Int. J. Robot. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1177\/0278364907079272","article-title":"Development of a tiny orientation estimation device to operate under motion and magnetic disturbance","volume":"26","author":"Harada","year":"2007","journal-title":"Int. J. Robot. Res."},{"key":"ref_25","unstructured":"Bouguet, J. Pyramidal Implementation of the Lucas Kanade Feature Tracker: Description of the Algorithm. Available online: http:\/\/robots.stanford.edu\/cs223b04\/algo_tracking.pdf (access on 22 November 2012)."},{"key":"ref_26","unstructured":"Lucas, B.D., and Kanade, T. (, January April). An Iterative Image Registration Technique with an Application to Stereo Vision. Vancouver, BC, Canada."},{"key":"ref_27","unstructured":"Shi, J., and Tomasi, C. (1994, January 21\u201323). Good Features to Track. Seattle, WA, USA."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Yang, Y., Qixin, C., Charles, L., and Zhen, Z. (2009, January 14\u201316). Pose Estimation Based on Four Coplanar Point Correspondences. Tianjin, China.","DOI":"10.1109\/FSKD.2009.310"},{"key":"ref_29","unstructured":"Abdel-Aziz, Y.I., and Karara, H.M. (, January January). Direct Linear Transformation from Comparator Coordinates into Object Space Coordinates in Close-Range Photogrammetry. Urbana, IL, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1109\/TAES.1970.310128","article-title":"Estimating optimal tracking filter performance for manned maneuvering targets","volume":"6","author":"Singer","year":"1970","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","first-page":"444","article-title":"Decentering distortion of lenses","volume":"32","author":"Brown","year":"1966","journal-title":"Photogramm. Eng."},{"key":"ref_32","unstructured":"Bouguet, J.Y. Camera Calibration Toolbox for Matlab. Available from: http:\/\/www.vision.caltech.edu\/bouguetj\/calib_doc\/ (accessed on 22 November 2012)."},{"key":"ref_33","unstructured":"Harris, C., and Stephens, M. (September, January 31). A combined Corner and Edge Detector. Manchester, UK."},{"key":"ref_34","first-page":"311","article-title":"Procedure for effortless in-field calibration of three-axial rate gyro and accelerometers","volume":"7","author":"Ferraris","year":"1995","journal-title":"Sens. Mater."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2657","DOI":"10.1109\/TBME.2010.2060723","article-title":"Zero-velocity detection\u2014An algorithm evaluation","volume":"57","author":"Skog","year":"2010","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2024","DOI":"10.1109\/TPAMI.2006.252","article-title":"Robust pose estimation from a planar target","volume":"28","author":"Schweighofer","year":"2006","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Dannilidis, K., and Nagel, H.H. (1993, January 15\u201317). The Coupling of Rotation and Translation in Motion Estimation of Planar Surfaces. New York, NY, USA.","DOI":"10.1109\/CVPR.1993.340990"},{"key":"ref_38","unstructured":"Bleser, G., and Stricker, D. (, January March). Advanced Tracking Through Efficient Image Processing and Visual-Inertial Sensor Fusion. Reno, NV, USA."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"8491","DOI":"10.3390\/s120708491","article-title":"Variable-state-dimension kalman-based filter for orientation determination using inertial and magnetic sensors","volume":"12","author":"Sabatini","year":"2012","journal-title":"Sensors"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1177\/0278364907079283","article-title":"Fast ego-motion estimation with multi-rate fusion of inertial and vision","volume":"26","author":"Armesto","year":"2007","journal-title":"Int. J. Robot. Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/2\/1919\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:44:45Z","timestamp":1760219085000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/2\/1919"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,4]]},"references-count":40,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,2]]}},"alternative-id":["s130201919"],"URL":"https:\/\/doi.org\/10.3390\/s130201919","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,4]]}}}