{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T14:55:35Z","timestamp":1788879335993,"version":"build-2803163510"},"reference-count":49,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2020,11,29]],"date-time":"2020-11-29T00:00:00Z","timestamp":1606608000000},"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>Tracking the kinematics of human movement usually requires the use of equipment that constrains the user within a room (e.g., optical motion capture systems), or requires the use of a conspicuous body-worn measurement system (e.g., inertial measurement units (IMUs) attached to each body segment). This paper presents a novel Lie group constrained extended Kalman filter to estimate lower limb kinematics using IMU and inter-IMU distance measurements in a reduced sensor count configuration. The algorithm iterates through the prediction (kinematic equations), measurement (pelvis height assumption\/inter-IMU distance measurements, zero velocity update for feet\/ankles, flat-floor assumption for feet\/ankles, and covariance limiter), and constraint update (formulation of hinged knee joints and ball-and-socket hip joints). The knee and hip joint angle root-mean-square errors in the sagittal plane for straight walking were 7.6\u00b12.6\u2218 and 6.6\u00b12.7\u2218, respectively, while the correlation coefficients were 0.95\u00b10.03 and 0.87\u00b10.16, respectively. Furthermore, experiments using simulated inter-IMU distance measurements show that performance improved substantially for dynamic movements, even at large noise levels (\u03c3=0.2 m). However, further validation is recommended with actual distance measurement sensors, such as ultra-wideband ranging sensors.<\/jats:p>","DOI":"10.3390\/s20236829","type":"journal-article","created":{"date-parts":[[2020,11,29]],"date-time":"2020-11-29T21:00:57Z","timestamp":1606683657000},"page":"6829","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Estimating Lower Limb Kinematics Using a Lie Group Constrained Extended Kalman Filter with a Reduced Wearable IMU Count and Distance Measurements"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0130-5570","authenticated-orcid":false,"given":"Luke Wicent F.","family":"Sy","sequence":"first","affiliation":[{"name":"Graduate School of Biomedical Engineering, UNSW Sydney, Sydney 2052, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1637-1079","authenticated-orcid":false,"given":"Nigel H.","family":"Lovell","sequence":"additional","affiliation":[{"name":"Graduate School of Biomedical Engineering, UNSW Sydney, Sydney 2052, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2630-5449","authenticated-orcid":false,"given":"Stephen J.","family":"Redmond","sequence":"additional","affiliation":[{"name":"UCD School of Electrical and Electronic Engineering, University College Dublin, Belfield, 4 Dublin, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Merriaux, P., Dupuis, Y., Boutteau, R., Vasseur, P., and Savatier, X. (2017). A Study of Vicon System Positioning Performance. Sensors, 17.","DOI":"10.3390\/s17071591"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Glowinski, S., \u0141osi\u0144ski, K., Kowia\u0144ski, P., Wa\u015bkow, M., Bryndal, A., and Grochulska, A. (2020). Inertial sensors as a tool for diagnosing discopathy lumbosacral pathologic gait: A preliminary research. Diagnostics, 10.","DOI":"10.3390\/diagnostics10060342"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rovini, E., Maremmani, C., and Cavallo, F. (2020). A wearable system to objectify assessment of motor tasks for supporting parkinson\u2019s disease diagnosis. Sensors, 20.","DOI":"10.3390\/s20092630"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1177\/0269215514543333","article-title":"Improvement in balance using a virtual reality-based stepping exercise: A randomized controlled trial involving individuals with chronic stroke","volume":"29","author":"Colomer","year":"2015","journal-title":"Clin. Rehabil."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Shull, P., Lurie, K., Shin, M., Besier, T., and Cutkosky, M. (2010, January 25\u201326). Haptic gait retraining for knee osteoarthritis treatment. Proceedings of the 2010 IEEE Haptics Symposium, Waltham, MA, USA.","DOI":"10.1109\/HAPTIC.2010.5444625"},{"key":"ref_6","first-page":"1","article-title":"Xsens MVN: Full 6DOF human motion tracking using miniature inertial sensors","volume":"3","author":"Roetenberg","year":"2009","journal-title":"Xsens Motion Technologies BV Tech. Rep."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9321","DOI":"10.3390\/s130709321","article-title":"Three dimensional gait analysis using wearable acceleration and gyro sensors based on quaternion calculations","volume":"13","author":"Tadano","year":"2013","journal-title":"Sensors"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1109\/JSEN.2016.2639530","article-title":"Robust Biomechanical Model-Based 3-D Indoor Localization and Tracking Method Using UWB and IMU","volume":"17","author":"Yoon","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"055101","DOI":"10.1088\/0957-0233\/23\/5\/055101","article-title":"Biomechanical model-based displacement estimation in micro-sensor motion capture","volume":"23","author":"Meng","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6008","DOI":"10.1109\/JSEN.2016.2574124","article-title":"Quaternion-based complementary filter for attitude determination of a smartphone","volume":"16","author":"Lovell","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9332","DOI":"10.1109\/JSEN.2018.2864989","article-title":"Computationally efficient adaptive error-state Kalman filter for attitude estimation","volume":"18","author":"Khamis","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1145\/1966394.1966397","article-title":"Motion reconstruction using sparse accelerometer data","volume":"30","author":"Tautges","year":"2011","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Huang, Y., Kaufmann, M., Aksan, E., Black, M.J., Hilliges, O., and Pons-Moll, G. (2018). Deep inertial poser: Learning to reconstruct human pose from sparse inertial measurements in real time. SIGGRAPH Asia 2018 Technical Papers, Tokyo, Japan, Association for Computing Machinery, Inc.","DOI":"10.1145\/3272127.3275108"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/TBME.2012.2223465","article-title":"A novel approach to reducing number of sensing units for wearable gait analysis systems","volume":"60","author":"Salarian","year":"2013","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sy, L.W., Raitor, M., Del Rosario, M.B., Khamis, H., Kark, L., Lovell, N.H., and Redmond, S.J. (2020). Estimating lower limb kinematics using a reduced wearable sensor count. IEEE Trans. Biomed. Eng., in press.","DOI":"10.1109\/TBME.2020.3026464"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1088\/0967-3334\/33\/12\/2099","article-title":"Human pose recovery using wireless inertial measurement units","volume":"33","author":"Lin","year":"2012","journal-title":"Physiol. Meas."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1111\/cgf.13131","article-title":"Sparse inertial poser: Automatic 3D human pose estimation from sparse IMUs","volume":"Volume 36","author":"Rosenhahn","year":"2017","journal-title":"Computer Graphics Forum"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Barfoot, T.D. (2017). State Estimation for Robotics, Cambridge University Press.","DOI":"10.1017\/9781316671528"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1109\/TRO.2006.878978","article-title":"Error propagation on the Euclidean group with applications to manipulator kinematics","volume":"22","author":"Wang","year":"2006","journal-title":"IEEE Trans. Robot."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1109\/TRO.2014.2298059","article-title":"Associating uncertainty with three-dimensional poses for use in estimation problems","volume":"30","author":"Barfoot","year":"2014","journal-title":"IEEE Trans. Robot."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10851-014-0517-0","article-title":"Continuous-discrete extended Kalman filter on matrix Lie groups using concentrated Gaussian distributions","volume":"51","author":"Bourmaud","year":"2014","journal-title":"J. Math. Imaging Vis."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Brossard, M., Bonnabel, S., and Condomines, J.P. (2017, January 24\u201328). Unscented Kalman filtering on Lie groups. Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8206066"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"\u0106esi\u0107, J., Joukov, V., Petrovi\u0107, I., and Kuli\u0107, D. (2016, January 15\u201317). Full body human motion estimation on lie groups using 3D marker position measurements. Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Cancun, Mexico.","DOI":"10.1109\/HUMANOIDS.2016.7803369"},{"key":"ref_24","first-page":"1","article-title":"Estimation and observability analysis of human motion on Lie groups","volume":"50","author":"Joukov","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Joukov, V., Cesic, J., Westermann, K., Markovic, I., Kulic, D., and Petrovic, I. (2017, January 24\u201328). Human motion estimation on Lie groups using IMU measurements. Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8206016"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hol, J.D., Dijkstra, F., Luinge, H., and Schon, T.B. (2009, January 9\u201311). Tightly coupled UWB\/IMU pose estimation. Proceedings of the 2009 IEEE International Conference on Ultra-Wideband, Vancouver, BC, Canada.","DOI":"10.1109\/ICUWB.2009.5288724"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Malleson, C., Gilbert, A., Trumble, M., Collomosse, J., and Hilton, A. (2017, January 10\u201312). Real-time full-body motion capture from video and IMUs. Proceedings of the International Conference on 3D Vision (3DV), Qingdao, China.","DOI":"10.1109\/3DV.2017.00058"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s11263-018-1118-y","article-title":"Fusing visual and inertial sensors with semantics for 3D human pose estimation","volume":"127","author":"Gilbert","year":"2019","journal-title":"Int. J. Comput. Vis."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Helten, T., Muller, M., Seidel, H.P., and Theobalt, C. (2013, January 8\u201312). Real-time body tracking with one depth camera and inertial sensors. Proceedings of the IEEE International Conference on Computer Vision, Sydney, Australia.","DOI":"10.1109\/ICCV.2013.141"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1145\/1276377.1276421","article-title":"Practical motion capture in everyday surroundings","volume":"26","author":"Vlasic","year":"2007","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Sy, L., Lovell, N.H., and Redmond, S.J. (2020, January 20\u201324). Estimating lower limb kinematics using distance measurements with a reduced wearable inertial sensor count. Proceedings of the 2020 42nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Montreal, QC, Canada.","DOI":"10.1109\/EMBC44109.2020.9175684"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sy, L., Lovell, N.H., and Redmond, S.J. (December, January 29). Estimating lower limb kinematics using a Lie group constrained EKF and a reduced wearable IMU count. Proceedings of the 2020 8th IEEE International Conference on Biomedical Robotics and Biomechatronics (Biorob), New York, NY, USA.","DOI":"10.1109\/BioRob49111.2020.9224342"},{"key":"ref_33","unstructured":"Selig, J.M. (2004). Lie groups and Lie algebras in robotics. Computational Noncommutative Algebra and Applications, Springer."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Stillwell, J. (2008). Naive Lie Theory, Springer Science & Business Media.","DOI":"10.1007\/978-0-387-78214-0"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chirikjian, G. (2012). Stochastic Models, Information Theory, and Lie Groups. II: Analytic Methods and Modern Applications, Springer Science & Business Media.","DOI":"10.1007\/978-0-8176-4944-9"},{"key":"ref_36","unstructured":"Bourmaud, G., Megret, R., Giremus, A., and Berthoumieu, Y. (2013, January 9\u201313). Discrete extended Kalman filter on Lie groups. Proceedings of the European Signal Processing Conference, Marrakech, Morocco."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Cloete, T., and Scheffer, C. (2008, January 20\u201325). Benchmarking of a full-body inertial motion capture system for clinical gait analysis. Proceedings of the 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, BC, Canada.","DOI":"10.1109\/IEMBS.2008.4650232"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Hu, X., Yao, C., and Soh, G.S. (2015, January 11\u201314). Performance evaluation of lower limb ambulatory measurement using reduced inertial measurement units and 3R gait model. Proceedings of the IEEE International Conference on Rehabilitation Robotics, Singapore.","DOI":"10.1109\/ICORR.2015.7281257"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Malajner, M., Planinsic, P., and Gleich, D. (2015, January 10\u201312). UWB ranging accuracy. Proceedings of the 2015 22nd International Conference on Systems, Signals and Image Processing, London, UK.","DOI":"10.1109\/IWSSIP.2015.7314177"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Ledergerber, A., and D\u2019Andrea, R. (2017, January 27\u201330). Ultra-wideband range measurement model with Gaussian processes. Proceedings of the 1st Annual IEEE Conference on Control Technology and Applications, Hawaii, HI, USA.","DOI":"10.1109\/CCTA.2017.8062738"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.gaitpost.2008.09.003","article-title":"The reliability of three-dimensional kinematic gait measurements: A systematic review","volume":"29","author":"McGinley","year":"2009","journal-title":"Gait Posture"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Jimenez, A.R., Seco, F., Prieto, J.C., and Guevara, J. (2010, January 11\u201312). Indoor Pedestrian navigation using an INS\/EKF framework for yaw drift reduction and a foot-mounted IMU. Proceedings of the 2010 7th Workshop on Positioning, Navigation and Communication, Dresden, Germany.","DOI":"10.1109\/WPNC.2010.5649300"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Zhang, W., Li, X., Wei, D., Ji, X., and Yuan, H. (2017, January 18\u201321). A foot-mounted PDR System Based on IMU\/EKF+HMM+ ZUPT+ZARU+HDR+compass algorithm. Proceedings of the 2017 International Conference on Indoor Positioning and Indoor Navigation, Sapporo, Japan.","DOI":"10.1109\/IPIN.2017.8115916"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Dotlic, I., Connell, A., Ma, H., Clancy, J., and McLaughlin, M. (2017, January 25\u201326). Angle of arrival estimation using decawave DW1000 integrated circuits. Proceedings of the 2017 14th Workshop on Positioning, Navigation and Communications, Bremen, Germany.","DOI":"10.1109\/WPNC.2017.8250079"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2093","DOI":"10.1109\/TVCG.2019.2898650","article-title":"Mo2Cap2: Real-time mobile 3D motion capture with a cap-mounted fisheye camera","volume":"25","author":"Xu","year":"2019","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Laidig, D., Schauer, T., and Seel, T. (2017, January 17\u201320). Exploiting kinematic constraints to compensate magnetic disturbances when calculating joint angles of approximate hinge joints from orientation estimates of inertial sensors. Proceedings of the IEEE International Conference on Rehabilitation Robotics, London, UK.","DOI":"10.1109\/ICORR.2017.8009375"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Eckhoff, K., Kok, M., Lucia, S., and Seel, T. (2020). Sparse magnetometer-free inertial motion tracking\u2014A condition for observability in double hinge joint systems. arXiv.","DOI":"10.1016\/j.ifacol.2020.12.403"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.gaitpost.2008.12.004","article-title":"Magnetic distortion in motion labs, implications for validating inertial magnetic sensors","volume":"29","author":"Veeger","year":"2009","journal-title":"Gait Posture"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Li, T., Wang, L., Li, Q., and Liu, T. (2020, January 6\u20139). Lower-body walking motion estimation using only two shank-mounted inertial measurement units (IMUs). Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Boston, MA, USA.","DOI":"10.1109\/AIM43001.2020.9158961"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6829\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:39:14Z","timestamp":1760179154000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6829"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,29]]},"references-count":49,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20236829"],"URL":"https:\/\/doi.org\/10.3390\/s20236829","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202011.0166.v1","asserted-by":"object"}]},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,29]]}}}