{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:27:34Z","timestamp":1769214454225,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,9,22]],"date-time":"2017-09-22T00:00:00Z","timestamp":1506038400000},"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>Measurement of the ground reaction forces (GRF) during walking is typically limited to laboratory settings, and only short observations using wearable pressure insoles have been reported so far. In this study, a new proxy measurement method is proposed to estimate the vertical component of the GRF (vGRF) from wearable accelerometer signals. The accelerations are used as the proxy variable. An orthogonal forward regression algorithm (OFR) is employed to identify the dynamic relationships between the proxy variables and the measured vGRF using pressure-sensing insoles. The obtained model, which represents the connection between the proxy variable and the vGRF, is then used to predict the latter. The results have been validated using pressure insoles data collected from nine healthy individuals under two outdoor walking tasks in non-laboratory settings. The results show that the vGRFs can be reconstructed with high accuracy (with an average prediction error of less than 5.0%) using only one wearable sensor mounted at the waist (L5, fifth lumbar vertebra). Proxy measures with different sensor positions are also discussed. Results show that the waist acceleration-based proxy measurement is more stable with less inter-task and inter-subject variability than the proxy measures based on forehead level accelerations. The proposed proxy measure provides a promising low-cost method for monitoring ground reaction forces in real-life settings and introduces a novel generic approach for replacing the direct determination of difficult to measure variables in many applications.<\/jats:p>","DOI":"10.3390\/s17102181","type":"journal-article","created":{"date-parts":[[2017,9,22]],"date-time":"2017-09-22T11:03:15Z","timestamp":1506078195000},"page":"2181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":48,"title":["A New Proxy Measurement Algorithm with Application to the Estimation of Vertical Ground Reaction Forces Using Wearable Sensors"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8588-5172","authenticated-orcid":false,"given":"Yuzhu","family":"Guo","sequence":"first","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"},{"name":"INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"},{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5977-8090","authenticated-orcid":false,"given":"Fabio","family":"Storm","sequence":"additional","affiliation":[{"name":"INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"},{"name":"Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]},{"given":"Yifan","family":"Zhao","sequence":"additional","affiliation":[{"name":"The EPSRC Centre for Innovative Manufacturing in Through-life Engineering Services, Cranfield University, Cranfield MK43 0AL, UK"}]},{"given":"Stephen","family":"Billings","sequence":"additional","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"},{"name":"INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2383-5724","authenticated-orcid":false,"given":"Aleksandar","family":"Pavic","sequence":"additional","affiliation":[{"name":"INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"},{"name":"Vibration Engineering Section, College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5215-1746","authenticated-orcid":false,"given":"Claudia","family":"Mazz\u00e0","sequence":"additional","affiliation":[{"name":"INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"},{"name":"Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]},{"given":"Ling-Zhong","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"},{"name":"INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF00266460","article-title":"The analysis of ground reaction forces in pathological gait secondary to disorders of the foot","volume":"7","author":"Claeys","year":"1983","journal-title":"Int. Orthop."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1080\/23335432.2016.1229135","article-title":"Relationship between sagittal plane kinematics, foot morphology and vertical forces applied to three regions of the foot","volume":"3","author":"Hannah","year":"2016","journal-title":"Int. Biomech."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1177\/03635465980260012801","article-title":"Characteristic ground-reaction forces in baseball pitching","volume":"26","author":"MacWilliams","year":"1998","journal-title":"Am. J. Sports Med."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1177\/0278364905058363","article-title":"Ground reference points in legged locomotion: Definitions, biological trajectories and control implications","volume":"24","author":"Popovic","year":"2005","journal-title":"Int. J. Robot. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"29393","DOI":"10.3390\/s151129393","article-title":"Feature selection and predictors of falls with foot force sensors using kNN-based algorithms","volume":"15","author":"Liang","year":"2015","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e46","DOI":"10.1016\/j.archger.2009.05.009","article-title":"The relationship of force output characteristics during a sit-to-stand movement with lower limb muscle mass and knee joint extension in the elderly","volume":"50","author":"Yamada","year":"2010","journal-title":"Arch. Gerontol. Geriatr."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1186\/s12984-016-0154-5","article-title":"Free-living gait characteristics in ageing and parkinson\u2019s disease: Impact of environment and ambulatory bout length","volume":"13","author":"Godfrey","year":"2016","journal-title":"J. NeuroEng. Rehabil."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10240","DOI":"10.3390\/s101110240","article-title":"A wearable ground reaction force sensor system and its application to the measurement of extrinsic gait variability","volume":"10","author":"Liu","year":"2010","journal-title":"Sensors"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1097\/00002060-200201000-00004","article-title":"Postural sway and active balance performance in highly active lower-limb amputees","volume":"81","author":"Buckley","year":"2002","journal-title":"Am. J. Phys. Med. Rehabil."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1123\/jab.14.1.93","article-title":"A device for simultaneous measurement of pressure and shear force distribution on the plantar surface of the foot","volume":"14","author":"Davis","year":"1998","journal-title":"J. Appl. Biomech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1186\/s12984-015-0081-x","article-title":"Estimation of ground reaction forces and ankle moment with multiple, low-cost sensors","volume":"12","author":"Jacobs","year":"2015","journal-title":"J. NeuroEng. Rehabil."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2693","DOI":"10.1016\/j.jbiomech.2014.05.007","article-title":"Ground reaction force estimation using an insole-type pressure mat and joint kinematics during walking","volume":"47","author":"Jung","year":"2014","journal-title":"J. Biomech."},{"key":"ref_13","unstructured":"Lawrence, T.L., and Schmidt, R.N. (November, January 30). Wireless in-shoe force system [for motor prosthesis]. Proceedings of the IEEE 19th Annual International Conference on Engineering in Medicine and Biology Society, Chicago, IL, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Morris, S.J., and Paradiso, J.A. (2002, January 23\u201326). Shoe-integrated sensor system for wireless gait analysis and real-time feedback. Proceedings of the Second Joint 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Societyon Engineering in Medicine and Biology, Huston, TX, USA.","DOI":"10.1109\/IEMBS.2002.1053379"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1109\/TNSRE.2005.847359","article-title":"Ambulatory measurement of ground reaction forces","volume":"13","author":"Veltink","year":"2005","journal-title":"IEEE Trans. Neural Syst. Rehabilit. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.gaitpost.2006.07.017","article-title":"Evaluation of instrumented shoes for ambulatory assessment of ground reaction forces","volume":"26","author":"Liedtke","year":"2007","journal-title":"Gait Posture"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1109\/TBME.2006.889769","article-title":"Ambulatory assessment of ankle and foot dynamics","volume":"54","author":"Schepers","year":"2007","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.gaitpost.2016.11.008","article-title":"25 years of lower limb joint kinematics by using inertial and magnetic sensors: A review of methodological approaches","volume":"51","author":"Picerno","year":"2017","journal-title":"Gait Posture"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2372","DOI":"10.1016\/j.jbiomech.2013.07.036","article-title":"Prediction of ground reaction forces during gait based on kinematics and a neural network model","volume":"46","author":"Oh","year":"2013","journal-title":"J. Biomech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1016\/j.jbiomech.2014.04.030","article-title":"Prediction of ground reaction forces and moments during various activities of daily living","volume":"47","author":"Fluit","year":"2014","journal-title":"J. Biomech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s11044-016-9537-4","article-title":"Prediction of ground reaction forces and moments during sports-related movements","volume":"39","author":"Skals","year":"2017","journal-title":"Multibody Syst. Dyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1207\/s15327841mpee0803_1","article-title":"A comparison of accelerometers for predicting energy expenditure and vertical ground reaction force in school-age children","volume":"8","author":"Garcia","year":"2004","journal-title":"Meas. Phys. Educ. Exerc. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Neugebauer, J.M., Collins, K.H., and Hawkins, D.A. (2014). Ground reaction force estimates from actigraph GT3X+ hip accelerations. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0099023"},{"key":"ref_24","first-page":"155","article-title":"Validity of an accelerometer as a vertical ground reaction force measuring device in healthy children and adolescents and in children and adolescents with osteogenesis imperfecta type I","volume":"14","author":"Veilleux","year":"2014","journal-title":"J. Musculoskelet Neuronal Interact."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Karatsidis, A., Bellusci, G., Schepers, H., De Zee, M., Andersen, M., and Veltink, P. (2017). Estimation of ground reaction forces and moments during gait using only inertial motion capture. Sensors, 17.","DOI":"10.3390\/s17010075"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.jsv.2009.01.001","article-title":"Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems","volume":"323","author":"Lang","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Billings, S.A. (2013). Nonlinear System Identification: Narmax Methods in the Time, Frequency, and Spatio-Temporal Domains, John Wiley & Sons Ltd.","DOI":"10.1002\/9781118535561"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1080\/00207721.2014.981237","article-title":"An iterative orthogonal forward regression algorithm","volume":"46","author":"Guo","year":"2015","journal-title":"Int. J. Syst. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.neucom.2015.08.022","article-title":"Ultra-orthogonal forward regression algorithms for the identification of non-linear dynamic systems","volume":"173","author":"Guo","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.gaitpost.2016.08.012","article-title":"Gait event detection in laboratory and real life settings: Accuracy of ankle and waist sensor based methods","volume":"50","author":"Storm","year":"2016","journal-title":"Gait Posture"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1049\/ip-d.1983.0034","article-title":"Structure detection and model validity tests in the identification of non-linear systems","volume":"130","author":"Billings","year":"1983","journal-title":"IEE Proc. D Control Theory Appl."},{"key":"ref_32","unstructured":"Estep, D. (2002). The weierstrass approximation theorem. Practical Analysis in One Variable, Springer."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.gaitpost.2005.12.017","article-title":"Gait event detection using linear accelerometers or angular velocity transducers in able-bodied and spinal-cord injured individuals","volume":"24","author":"Jasiewicz","year":"2006","journal-title":"Gait Posture"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.gaitpost.2003.10.001","article-title":"Assessment and validation of a simple automated method for the detection of gait events and intervals","volume":"20","author":"Ghoussayni","year":"2004","journal-title":"Gait Posture"},{"key":"ref_35","unstructured":"Volterra, V. (1959). Theory of Functionals and of Integral and Integro-Differential Equation, Dover."},{"key":"ref_36","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_37","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1002\/jor.1100070611","article-title":"Repeatability of kinematic, kinetic, and electromyographic data in normal adult gait","volume":"7","author":"Kadaba","year":"1989","journal-title":"J. Orthop. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1016\/0021-9290(91)90002-5","article-title":"Calculation of vertical ground reaction force estimates during running from positional data","volume":"24","author":"Bobbert","year":"1991","journal-title":"J. Biomech."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1016\/j.jbiomech.2004.04.030","article-title":"Dynamic analysis of load carriage biomechanics during level walking","volume":"38","author":"Ren","year":"2005","journal-title":"J. Biomech."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/j.jbiomech.2010.10.045","article-title":"Optimization-based prediction of asymmetric human gait","volume":"44","author":"Xiang","year":"2011","journal-title":"J. Biomech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3776","DOI":"10.1016\/j.jbiomech.2015.08.027","article-title":"Computation of ground reaction force using zero moment point","volume":"48","author":"Dijkstra","year":"2015","journal-title":"J. Biomech."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.jbiomech.2009.01.033","article-title":"Lower extremity joint torque predicted by using artificial neural network during vertical jump","volume":"42","author":"Liu","year":"2009","journal-title":"J. Biomech."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1016\/j.jbiomech.2011.11.057","article-title":"A neural network model to predict knee adduction moment during walking based on ground reaction force and anthropometric measurements","volume":"45","author":"Favre","year":"2012","journal-title":"J. Biomech."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1186\/1743-0003-5-30","article-title":"Control of the upper body accelerations in young and elderly women during level walking","volume":"5","author":"Mazza","year":"2008","journal-title":"J. Neuroeng. Rehabil."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s00702-014-1279-y","article-title":"New evidence for gait abnormalities among parkinson\u2019s disease patients who suffer from freezing of gait: Insights using a body-fixed sensor worn for 3 days","volume":"122","author":"Weiss","year":"2015","journal-title":"J. Neural Transm."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/10\/2181\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:45:37Z","timestamp":1760208337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/10\/2181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,22]]},"references-count":45,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["s17102181"],"URL":"https:\/\/doi.org\/10.3390\/s17102181","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,22]]}}}