{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T16:01:01Z","timestamp":1768924861968,"version":"3.49.0"},"reference-count":49,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T00:00:00Z","timestamp":1603843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["J2-8172"],"award-info":[{"award-number":["J2-8172"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P2-0228"],"award-info":[{"award-number":["P2-0228"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["731931"],"award-info":[{"award-number":["731931"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Estimation of the centre of pressure (COP) is an important part of the gait analysis, for example, when evaluating the functional capacity of individuals affected by motor impairment. Inertial measurement units (IMUs) and force sensors are commonly used to measure gait characteristic of healthy and impaired subjects. We present a methodology for estimating the COP solely from raw gyroscope, accelerometer, and magnetometer data from IMUs using statistical modelling. We demonstrate the viability of the method using an example of two models: a linear model and a non-linear Long-Short-Term Memory (LSTM) neural network model. Models were trained on the COP ground truth data measured using an instrumented treadmill and achieved the average intra-subject root mean square (RMS) error between estimated and ground truth COP of 12.3 mm and the average inter-subject RMS error of 23.7 mm which is comparable or better than similar studies so far. We show that the calibration procedure in the instrumented treadmill can be as short as a couple of minutes without the decrease in our model performance. We also show that the magnetic component of the recorded IMU signal, which is most sensitive to environmental changes, can be safely dropped without a significant decrease in model performance. Finally, we show that the number of IMUs can be reduced to five without deterioration in the model performance.<\/jats:p>","DOI":"10.3390\/s20216136","type":"journal-article","created":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T21:21:00Z","timestamp":1604006460000},"page":"6136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Centre of Pressure Estimation during Walking Using Only Inertial-Measurement Units and End-To-End Statistical Modelling"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9359-0297","authenticated-orcid":false,"given":"Janez","family":"Podobnik","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1633-4681","authenticated-orcid":false,"given":"David","family":"Kralji\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2746-6890","authenticated-orcid":false,"given":"Matja\u017e","family":"Zadravec","sequence":"additional","affiliation":[{"name":"Research and Development Unit, University Rehabilitation Institute Republic of Slovenia, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marko","family":"Munih","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e627","DOI":"10.1161\/STROKEAHA.109.558940","article-title":"Overground Physical Therapy Gait Training for Chronic Stroke Patients With Mobility Deficits","volume":"40","author":"States","year":"2009","journal-title":"Stroke"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.gaitpost.2017.06.019","article-title":"A systematic review of gait analysis methods based on inertial sensors and adaptive algorithms","volume":"57","author":"Caldas","year":"2017","journal-title":"Gait Posture"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6","DOI":"10.7243\/2055-2386-4-6","article-title":"Biomechanical parameters for gait analysis: a systematic review of healthy human gait","volume":"4","author":"Roberts","year":"2017","journal-title":"Phys. Ther. Rehabil."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ancillao, A., Tedesco, S., Barton, J., and O\u2019Flynn, B. (2018). Indirect Measurement of Ground Reaction Forces and Moments by Means of Wearable Inertial Sensors: A Systematic Review. Sensors, 18.","DOI":"10.3390\/s18082564"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2979","DOI":"10.1109\/TIM.2009.2016801","article-title":"Human Gait Acquisition and Characterization","volume":"58","author":"Ferreira","year":"2009","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0966-6362(96)82849-9","article-title":"Human balance and posture control during standing and walking","volume":"3","author":"Winter","year":"1995","journal-title":"Gait Posture"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Karatsidis, A., Bellusci, G., Schepers, H.M., De Zee, M., Andersen, M.S., and Veltink, P.H. (2017). Estimation of Ground Reaction Forces and Moments During Gait Using Only Inertial Motion Capture. Sensors, 17.","DOI":"10.3390\/s17010075"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Shahabpoor, E., and Pavic, A. (2017). Measurement of Walking Ground Reactions in Real-Life Environments: A Systematic Review of Techniques and Technologies. Sensors, 17.","DOI":"10.3390\/s17092085"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1109\/TIM.2013.2245185","article-title":"Metrological Performances of a Plantar Pressure Measurement System","volume":"62","author":"Saggin","year":"2013","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1109\/TIM.2012.2183035","article-title":"Design of an Unobtrusive Reaction Force Measurement and Its Application on Treadmills","volume":"61","author":"Chen","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1016\/j.jbiomech.2006.04.016","article-title":"Experimental verification of a computational technique for determining ground reactions in human bipedal stance","volume":"40","author":"Audu","year":"2007","journal-title":"J. Biomech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2750","DOI":"10.1016\/j.jbiomech.2008.06.001","article-title":"Whole body inverse dynamics over a complete gait cycle based only on measured kinematics","volume":"41","author":"Ren","year":"2008","journal-title":"J. Biomech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.gaitpost.2016.01.005","article-title":"Dynamically adjustable foot-ground contact model to estimate ground reaction force during walking and running","volume":"45","author":"Jung","year":"2016","journal-title":"Gait Posture"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1016\/j.clinbiomech.2004.04.005","article-title":"Applications of artificial neural nets in clinical biomechanics","volume":"19","year":"2004","journal-title":"Clin. Biomech."},{"key":"ref_15","unstructured":"Funk, C., Nagendra, S., Scott, J., Ravichandran, B., Challis, J.H., Collins, R.T., and Liu, Y. (2019). Learning Dynamics from Kinematics: Estimating 2D Foot Pressure Maps from Video Frames. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.gaitpost.2016.01.018","article-title":"Calibration of an instrumented treadmill using a precision-controlled device with artificial neural network-based error corrections","volume":"45","author":"Hsieh","year":"2016","journal-title":"Gait Posture"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2714","DOI":"10.1109\/TIM.2018.2829338","article-title":"A 6 DoF, Wearable, Compliant Shoe Sensor for Total Ground Reaction Measurement","volume":"67","author":"Eng","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Choi, H.S., Lee, C.H., Shim, M., Han, J.I., and Baek, Y.S. (2018). Design of an Artificial Neural Network Algorithm for a Low-Cost Insole Sensor to Estimate the Ground Reaction Force (GRF) and Calibrate the Center of Pressure (CoP). Sensors, 18.","DOI":"10.3390\/s18124349"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1109\/TIM.2015.2504078","article-title":"Using Distributed Wearable Sensors to Measure and Evaluate Human Lower Limb Motions","volume":"65","author":"Qiu","year":"2016","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Brognara, L., Palumbo, P., Grimm, B., and Palmerini, L. (2019). Assessing Gait in Parkinson\u2019s Disease Using Wearable Motion Sensors: A Systematic Review. Diseases, 7.","DOI":"10.3390\/diseases7010018"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2628","DOI":"10.1016\/j.jbiomech.2008.06.023","article-title":"Online gait event detection using a large force platform embedded in a treadmill","volume":"41","author":"Roerdink","year":"2008","journal-title":"J. Biomech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1007\/s11517-014-1195-1","article-title":"Gaitography applied to prosthetic walking","volume":"52","author":"Roerdink","year":"2014","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zadravec, M., Olen\u0161ek, A., Rudolf, M., Bizovi\u010dar, N., Goljar, N., and Matja\u010di\u0107, Z. (2017, January 17\u201320). A novel robot-assisted training approach for improving gait symmetry after stroke. Proceedings of the 2017 International Conference on Rehabilitation Robotics (ICORR), London, UK.","DOI":"10.1109\/ICORR.2017.8009250"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1111\/jar.12462","article-title":"Identification of spatiotemporal gait parameters and pressure-related characteristics in children with Angelman syndrome: A pilot study","volume":"31","author":"Grieco","year":"2018","journal-title":"J. Appl. Res. Intellect. Disabil."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1881","DOI":"10.1016\/j.jbiomech.2004.08.015","article-title":"Determining the centre of pressure during walking and running using an instrumented treadmill","volume":"38","author":"Verkerke","year":"2005","journal-title":"J. Biomech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"e4640","DOI":"10.7717\/peerj.4640","article-title":"A public dataset of overground and treadmill walking kinematics and kinetics in healthy individuals","volume":"6","author":"Fukuchi","year":"2018","journal-title":"PeerJ"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1186\/s12984-016-0160-7","article-title":"A novel robot for imposing perturbations during overground walking: mechanism, control and normative stepping responses","volume":"13","author":"Zadravec","year":"2016","journal-title":"J. Neuroeng. Rehabil."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Matja\u010di\u0107, Z., Zadravec, M., and Olen\u0161ek, A. (2019). Influence of Treadmill Speed and Perturbation Intensity on Selection of Balancing Strategies during Slow Walking Perturbed in the Frontal Plane. Appl. Bionics Biomech., 2019.","DOI":"10.1155\/2019\/1046459"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1016\/S0021-9290(00)00101-9","article-title":"Active control of lateral balance in human walking","volume":"33","author":"Bauby","year":"2000","journal-title":"J. Biomech."},{"key":"ref_30","unstructured":"Carrozza, M.C., Micera, S., and Pons, J.L. (2019). Wearable Sensory Apparatus Performance While Using Inertial Measurement Units. Wearable Robotics: Challenges and Trends, Springer International Publishing."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1016\/j.medengphy.2013.07.003","article-title":"Automated detection of gait initiation and termination using wearable sensors","volume":"35","author":"Novak","year":"2013","journal-title":"Med. Eng. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"18800","DOI":"10.3390\/s141018800","article-title":"Toward Real-Time Automated Detection of Turns during Gait Using Wearable Inertial Measurement Units","volume":"14","author":"Novak","year":"2014","journal-title":"Sensors"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/S0167-9457(96)00052-8","article-title":"Three-dimensional motion of the center of gravity of the body during walking","volume":"16","author":"Whittle","year":"1997","journal-title":"Hum. Mov. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0268-0033(95)91394-T","article-title":"Position and orientation in space of bones during movement: Anatomical frame definition and determination","volume":"10","author":"Cappozzo","year":"1995","journal-title":"Clin. Biomech."},{"key":"ref_35","unstructured":"Graf, B. (2008). Quaternions and dynamics. arXiv."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"70","DOI":"10.2514\/3.19717","article-title":"Three-axis attitude determination from vector observations","volume":"4","author":"Shuster","year":"1981","journal-title":"J. Guid. Control."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-Term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_38","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., and Devin, M. (2015). TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. arXiv."},{"key":"ref_39","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_40","unstructured":"Lipton, Z.C., Berkowitz, J., and Elkan, C. (2015). A critical review of recurrent neural networks for sequence learning. arXiv."},{"key":"ref_41","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A Method for Stochastic Optimization. arXiv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.jbiomech.2018.07.039","article-title":"Validation of gait event detection by centre of pressure during target stepping in healthy and paretic gait","volume":"79","author":"Hammerbeck","year":"2018","journal-title":"J. Biomech."},{"key":"ref_43","unstructured":"Spelitz, S. (2020). BrainGait: Gait Event Detection and Visualization for Robotic Rehabilitation. [Master\u2019s Thesis, Research Unit of Computer Graphics, Institute of Visual Computing and Human-Centered Technology, Faculty of Informatics, Technische Universit\u00e4t Wien]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1177\/0309364618791618","article-title":"Gaitography on lower-limb amputees: Repeatability and between-methods agreement","volume":"43","author":"Timmermans","year":"2019","journal-title":"Prosthetics Orthot. Int."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3103","DOI":"10.1016\/j.proeng.2010.04.118","article-title":"A multimodal approach for insole motion measurement and analysis","volume":"2","author":"Jagos","year":"2010","journal-title":"Procedia Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1080\/03091902.2017.1320434","article-title":"Mobile gait analysis via eSHOEs instrumented shoe insoles: A pilot study for validation against the gold standard GAITRite\u00ae","volume":"41","author":"Jagos","year":"2017","journal-title":"J. Med. Eng. Technol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1109\/TNSRE.2018.2885309","article-title":"Gait and Dynamic Balance Sensing Using Wearable Foot Sensors","volume":"27","author":"Refai","year":"2019","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/S0021-9290(02)00008-8","article-title":"Spatio-temporal parameters of gait measured by an ambulatory system using miniature gyroscopes","volume":"35","author":"Aminian","year":"2002","journal-title":"J. Biomech."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1765","DOI":"10.1109\/JBHI.2018.2865218","article-title":"IMU-Based Classification of Parkinson\u2019s Disease From Gait: A Sensitivity Analysis on Sensor Location and Feature Selection","volume":"22","author":"Caramia","year":"2018","journal-title":"IEEE J. Biomed. Health Informatics"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/6136\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:30:03Z","timestamp":1760178603000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/6136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,28]]},"references-count":49,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20216136"],"URL":"https:\/\/doi.org\/10.3390\/s20216136","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,28]]}}}