{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T15:10:20Z","timestamp":1780672220483,"version":"3.54.1"},"reference-count":26,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["287295"],"award-info":[{"award-number":["287295"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["323472"],"award-info":[{"award-number":["323472"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Vertical ground reaction force (vGRF) can be measured by force plates or instrumented treadmills, but their application is limited to indoor environments. Insoles remove this restriction but suffer from low durability (several hundred hours). Therefore, interest in the indirect estimation of vGRF using inertial measurement units and machine learning techniques has increased. This paper presents a methodology for indirectly estimating vGRF and other features used in gait analysis from measurements of a wearable GPS-aided inertial navigation system (INS\/GPS) device. A set of 27 features was extracted from the INS\/GPS data. Feature analysis showed that six of these features suffice to provide precise estimates of 11 different gait parameters. Bagged ensembles of regression trees were then trained and used for predicting gait parameters for a dataset from the test subject from whom the training data were collected and for a dataset from a subject for whom no training data were available. The prediction accuracies for the latter were significantly worse than for the first subject but still sufficiently good. K-nearest neighbor (KNN) and long short-term memory (LSTM) neural networks were then used for predicting vGRF and ground contact times. The KNN yielded a lower normalized root mean square error than the neural network for vGRF predictions but cannot detect new patterns in force curves.<\/jats:p>","DOI":"10.3390\/s21041553","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T20:19:36Z","timestamp":1614111576000},"page":"1553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Indirect Estimation of Vertical Ground Reaction Force from a Body-Mounted INS\/GPS Using Machine Learning"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5601-0131","authenticated-orcid":false,"given":"Dharmendra","family":"Sharma","sequence":"first","affiliation":[{"name":"VTT Technical Research Centre of Finland, Kaitov\u00e4yl\u00e4 1, 90570 Oulu, Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2617-3156","authenticated-orcid":false,"given":"Pavel","family":"Davidson","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4314-7339","authenticated-orcid":false,"given":"Philipp","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1158-6951","authenticated-orcid":false,"given":"Robert","family":"Pich\u00e9","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","unstructured":"Arafsha, F., Hanna, C., Aboualmagd, A., Fraser, S., and El Saddik, A. (2018). Instrumented Wireless SmartInsole System for Mobile Gait Analysis: A Validation Pilot Study with Tekscan Strideway. J. Sens. Actuator Netw., 7.","DOI":"10.3390\/jsan7030036"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1080\/02640414.2016.1161205","article-title":"Validation of Moticon\u2019s OpenGo sensor insoles during gait, jumps, balance and cross-country skiing specific imitation movements","volume":"35","author":"Martiner","year":"2017","journal-title":"J. Sports Sci."},{"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":"915","DOI":"10.1016\/j.asoc.2017.09.027","article-title":"Real-time human activity recognition from accelerometer data using Convolutional Neural Networks","volume":"62","author":"Ignatov","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"218","DOI":"10.3389\/fphys.2018.00218","article-title":"Estimation of Vertical Ground Reaction Forces and Sagittal Knee Kinematics during Running Using Three Inertial Sensors","volume":"9","author":"Wouda","year":"2018","journal-title":"Front. Physiol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.jbiomech.2018.06.006","article-title":"Estimation of vertical ground reaction force during running using neural network model and uniaxial accelerometer","volume":"76","author":"Ngoh","year":"2018","journal-title":"J. Biomech."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Dehzangi, O., Taherisadr, M., and Changal Vala, R. (2017). IMU-Based Gait Recognition Using Convolutional Neural Networks and Multi-Sensor Fusion. Sensors, 17.","DOI":"10.3390\/s17122735"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jiang, X., Napier, C., Hannigan, B., Eng, J.J., and Menon, C. (2020). Estimating Vertical Ground Reaction Force during Walking Using a Single Inertial Sensor. Sensors, 20.","DOI":"10.3390\/s20154345"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Johnson, W.R., Mian, A., Robinson, M.A., Verheul, J., Lloyd, D.G., and Alderson, J.A. (2020). Multidimensional ground reaction forces and moments from wearable sensor accelerations via deep learning. IEEE Trans. Biomed. Eng.","DOI":"10.1109\/TBME.2020.3006158"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Guo, Y., Storm, F., Zhao, Y., Billings, S.A., Pavic, A., Mazz\u00e0, C., and Guo, L.-Z. (2017). A new proxy measurement algorithm with application to the estimation of vertical ground reaction forces using wearable sensors. Sensors, 17.","DOI":"10.3390\/s17102181"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Davidson, P., Virekunnas, H., Sharma, D., Pich\u00e9, R., and Cronin, N. (2019). Continuous analysis of running mechanics by means of an integrated INS\/GPS device. Sensors, 19.","DOI":"10.3390\/s19061480"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lim, H., Kim, B., and Park, S. (2020). Prediction of Lower Limb Kinetics and Kinematics during Walking by a Single IMU on the Lower Back Using Machine Learning. Sensors, 20.","DOI":"10.3390\/s20010130"},{"key":"ref_14","unstructured":"(2017). Moticon-ORTHO_booklet_en_print_01.01.02, Moticon GmbH."},{"key":"ref_15","unstructured":"(2017). Moticon_Insole-Instruction-Manual_1.3, Moticon GmbH. Version 1.3."},{"key":"ref_16","unstructured":"Ferri, M. (2021, January 18). Math for Sprinters\u2014Step Frequency and Stride Length. Available online: https:\/\/www.econathletes.com\/post\/math-for-sprinters-steps-per-second-and-stride-length."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Davidson, P., and Pich\u00e9, R. (2017, January 16\u201318). A method for post-mission velocity and orientation estimation based on data fusion from MEMS-IMU and GNSS. Proceedings of the IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI), Daegu, Korea.","DOI":"10.1109\/MFI.2017.8170383"},{"key":"ref_18","unstructured":"Sharma, D. (2019). Application of Machine Learning Methods for Human Gait Analysis. [Master\u2019s Thesis, Tampere University]. Available online: http:\/\/urn.fi\/URN:NBN:fi:tuni-201909093212."},{"key":"ref_19","unstructured":"Gallian, J. (2010). Biomechanics of Running and Walking. Mathematics and Sports, Mathematical Association of America."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Skiena, S.S. (2017). The Data Science Design Manual, Springer.","DOI":"10.1007\/978-3-319-55444-0"},{"key":"ref_21","unstructured":"Duda, R.O., Hart, P.E., and Stork, D.G. (2001). Pattern Classification, Wiley-Interscience. [2nd ed.]."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/j.1748-1716.1989.tb08655.x","article-title":"Ground reaction forces at different speeds of human walking and running","volume":"136","author":"Nilsson","year":"1989","journal-title":"Acta Physiol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Abidin, T., and Perrizo, W. (2006, January 23\u201327). SMART-TV: A fast and scalable nearest neighbor based classifier for data mining. Proceedings of the 2006 ACM symposium on Applied computing (SAC \u201906), Dijon, France.","DOI":"10.1145\/1141277.1141403"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1145\/361002.361007","article-title":"Multidimensional binary search trees used for associative searching","volume":"18","author":"Bentley","year":"1975","journal-title":"Commun. ACM"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Leporace, G., Batista, L.A., Metsavaht, L., and Nadal, J. (2015, January 25\u201329). Residual analysis of ground reaction forces simulation during gait using neural networks with different configurations. Proceedings of the 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Milano, Italy.","DOI":"10.1109\/EMBC.2015.7318976"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"610","DOI":"10.3389\/fphys.2018.00610","article-title":"Accurate estimation of running temporal parameters using foot-worn inertial sensors","volume":"9","author":"Falbriard","year":"2018","journal-title":"Front. Physiol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/4\/1553\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:27:15Z","timestamp":1760160435000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/4\/1553"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,23]]},"references-count":26,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["s21041553"],"URL":"https:\/\/doi.org\/10.3390\/s21041553","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,23]]}}}