{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T02:04:33Z","timestamp":1769220273428,"version":"3.49.0"},"reference-count":109,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T00:00:00Z","timestamp":1698192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100008749","name":"American College of Sports Medicine","doi-asserted-by":"publisher","award":["18-00671"],"award-info":[{"award-number":["18-00671"]}],"id":[{"id":"10.13039\/100008749","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008749","name":"American College of Sports Medicine","doi-asserted-by":"publisher","award":["G2018031595024439"],"award-info":[{"award-number":["G2018031595024439"]}],"id":[{"id":"10.13039\/100008749","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008749","name":"American College of Sports Medicine","doi-asserted-by":"publisher","award":["CGSD3-502358-2017"],"award-info":[{"award-number":["CGSD3-502358-2017"]}],"id":[{"id":"10.13039\/100008749","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Sigma Xi Scientific Research Honor Society","award":["18-00671"],"award-info":[{"award-number":["18-00671"]}]},{"name":"Sigma Xi Scientific Research Honor Society","award":["G2018031595024439"],"award-info":[{"award-number":["G2018031595024439"]}]},{"name":"Sigma Xi Scientific Research Honor Society","award":["CGSD3-502358-2017"],"award-info":[{"award-number":["CGSD3-502358-2017"]}]},{"name":"University of California Davis Library\u2019s Open Access Fund","award":["18-00671"],"award-info":[{"award-number":["18-00671"]}]},{"name":"University of California Davis Library\u2019s Open Access Fund","award":["G2018031595024439"],"award-info":[{"award-number":["G2018031595024439"]}]},{"name":"University of California Davis Library\u2019s Open Access Fund","award":["CGSD3-502358-2017"],"award-info":[{"award-number":["CGSD3-502358-2017"]}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["18-00671"],"award-info":[{"award-number":["18-00671"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["G2018031595024439"],"award-info":[{"award-number":["G2018031595024439"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["CGSD3-502358-2017"],"award-info":[{"award-number":["CGSD3-502358-2017"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Maury L Hull Endowed Fellowship for Musculoskeletal Biomechanics Research","award":["18-00671"],"award-info":[{"award-number":["18-00671"]}]},{"name":"Maury L Hull Endowed Fellowship for Musculoskeletal Biomechanics Research","award":["G2018031595024439"],"award-info":[{"award-number":["G2018031595024439"]}]},{"name":"Maury L Hull Endowed Fellowship for Musculoskeletal Biomechanics Research","award":["CGSD3-502358-2017"],"award-info":[{"award-number":["CGSD3-502358-2017"]}]},{"name":"University of California Davis Professors for the Future Fellowship","award":["18-00671"],"award-info":[{"award-number":["18-00671"]}]},{"name":"University of California Davis Professors for the Future Fellowship","award":["G2018031595024439"],"award-info":[{"award-number":["G2018031595024439"]}]},{"name":"University of California Davis Professors for the Future Fellowship","award":["CGSD3-502358-2017"],"award-info":[{"award-number":["CGSD3-502358-2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Twenty-seven methods of estimating vertical ground reaction force first peak, loading rate, second peak, average, and\/or time series from a single wearable accelerometer worn on the shank or approximate center of mass during running were compared. Force estimation errors were quantified for 74 participants across different running surfaces, speeds, and foot strike angles and biases, repeatability coefficients, and limits of agreement were modeled with linear mixed effects to quantify the accuracy, reliability, and precision. Several methods accurately and reliably estimated the first peak and loading rate, however, none could do so precisely (the limits of agreement exceeded \u00b165% of target values). Thus, we do not recommend first peak or loading rate estimation from accelerometers with the methods currently available. In contrast, the second peak, average, and time series could all be estimated accurately, reliably, and precisely with several different methods. Of these, we recommend the \u2018Pogson\u2019 methods due to their accuracy, reliability, and precision as well as their stability across surfaces, speeds, and foot strike angles.<\/jats:p>","DOI":"10.3390\/s23218719","type":"journal-article","created":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T07:22:15Z","timestamp":1698304935000},"page":"8719","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Acceleration-Based Estimation of Vertical Ground Reaction Forces during Running: A Comparison of Methods across Running Speeds, Surfaces, and Foot Strike Patterns"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4479-3909","authenticated-orcid":false,"given":"Dovin","family":"Kiernan","sequence":"first","affiliation":[{"name":"Biomedical Engineering Graduate Group, University of California, Davis, Davis, CA 95616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brandon","family":"Ng","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, University of California, Davis, Davis, CA 95616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5930-9844","authenticated-orcid":false,"given":"David A.","family":"Hawkins","sequence":"additional","affiliation":[{"name":"Biomedical Engineering Graduate Group, University of California, Davis, Davis, CA 95616, USA"},{"name":"Department of Neurobiology, Physiology, & Behavior, University of California, Davis, Davis, CA 95616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/S0021-9290(99)00048-2","article-title":"The effect of muscle stiffness and damping on simulated impact force peaks during running","volume":"32","author":"Nigg","year":"1999","journal-title":"J. Biomech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.jsams.2012.08.002","article-title":"Differences in kinetic variables between injured and noninjured novice runners: A prospective cohort study","volume":"16","author":"Bredeweg","year":"2013","journal-title":"J. Sci. Med. Sport"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1097\/00005768-199908000-00002","article-title":"Ground reaction forces, bone characteristics, and tibial stress fracture in male runners","volume":"31","author":"Crossley","year":"1999","journal-title":"Med. Sci. Sport. Exerc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1136\/bjsports-2015-094924","article-title":"Do runners who suffer injuries have higher vertical ground reaction forces than those who remain injury free? A systematic review and meta-analysis","volume":"50","author":"Vrielink","year":"2016","journal-title":"Br. J. Sports Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.clinbiomech.2010.08.005","article-title":"The relationship between lower extremity stress fractures and the ground reaction force: A systematic review","volume":"26","author":"Zadpoor","year":"2011","journal-title":"Clin. Biomech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1177\/03635465211063909","article-title":"Spatiotemporal and Ground-Reaction Force Characteristics as Risk Factors for Running-Related Injury: A Secondary Analysis of a Randomized Trial Including 800+ Recreational Runners","volume":"50","author":"Malisoux","year":"2022","journal-title":"Am. J. Sports Med."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jbiomech.2018.04.001","article-title":"Accelerometer-based prediction of running injury in National Collegiate Athletic Association track athletes","volume":"73","author":"Kiernan","year":"2018","journal-title":"J. Biomech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1007\/s40279-019-01110-z","article-title":"Biomechanical Risk Factors Associated with Running-Related Injuries: A Systematic Review","volume":"49","author":"Ceyssens","year":"2019","journal-title":"Sports Med."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1097\/JSM.0b013e3181b8c270","article-title":"Biomechanical and anatomic factors associated with a history of plantar fasciitis in female runners","volume":"19","author":"Pohl","year":"2009","journal-title":"Clin. J. Sport Med."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.humov.2016.01.013","article-title":"Comparison of ankle kinematics and ground reaction forces between prospectively injured and uninjured collegiate cross country runners","volume":"47","author":"Kuhman","year":"2016","journal-title":"Hum. Mov. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1123\/jab.2016-0356","article-title":"Association of Sprint Performance With Ground Reaction Forces During Acceleration and Maximal Speed Phases in a Single Sprint","volume":"34","author":"Nagahara","year":"2016","journal-title":"J. Appl. Biomech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3149","DOI":"10.1016\/j.jbiomech.2015.07.009","article-title":"Acceleration capability in elite sprinters and ground impulse: Push more, brake less?","volume":"48","author":"Morin","year":"2015","journal-title":"J. Biomech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1111\/sms.12389","article-title":"Sprint mechanics in world-class athletes: A new insight into the limits of human locomotion","volume":"25","author":"GRabita","year":"2015","journal-title":"Scand. J. Med. Sci. Sports"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1519\/JSC.0000000000001535","article-title":"Mechanical Determinants of Faster Change of Direction Speed Performance in Male Athletes","volume":"31","author":"Thomas","year":"2017","journal-title":"J. Strength Cond. Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kiernan, D., Dunn Siino, K., and Hawkins, D.A. (2023). Unsupervised Gait Event Identification with a Single Wearable Accelerometer and\/or Gyroscope: A Comparison of Methods across Running Speeds, Surfaces, and Foot Strike Patterns. Sensors, 23.","DOI":"10.3390\/s23115022"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e12752","DOI":"10.7717\/peerj.12752","article-title":"Predicting continuous ground reaction forces from accelerometers during uphill and downhill running: A recurrent neural network solution","volume":"10","author":"Alcantara","year":"2022","journal-title":"PeerJ"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1242\/jeb.106518","article-title":"Biomechanics and energetics of running on uneven terrain","volume":"218","author":"Voloshina","year":"2015","journal-title":"J. Exp. Biol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1080\/14763141.2016.1212917","article-title":"Ground reaction forces during steeplechase hurdling and waterjumps","volume":"16","author":"Kipp","year":"2017","journal-title":"Sports Biomech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1007\/s00421-020-04437-y","article-title":"Steep (30\u00b0) uphill walking vs. running: COM movements, stride kinematics, and leg muscle excitations","volume":"120","author":"Whiting","year":"2020","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1249\/MSS.0000000000002288","article-title":"Comparison of Tibial Shock during Treadmill and Teal-World Running","volume":"52","author":"Johnson","year":"2020","journal-title":"Med. Sci. Sport. Exerc."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1109\/TNSRE.2003.818185","article-title":"Design, development, and characteristics of an in-shoe triaxial pressure measurement transducer utilizing a single element of piezoelectric copolymer film","volume":"11","author":"Razian","year":"2003","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.apergo.2015.08.011","article-title":"Validity and reliability of pressure-measurement insoles for vertical ground reaction force assessment in field situations","volume":"53","author":"Koch","year":"2016","journal-title":"Appl. Ergon."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.gaitpost.2016.01.026","article-title":"Validity and repeatability of three in-shoe pressure measurement systems","volume":"46","author":"Price","year":"2016","journal-title":"Gait Posture"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1016\/j.jbiomech.2003.12.016","article-title":"Use of pressure insoles to calculate the complete ground reaction forces","volume":"37","author":"Cordero","year":"2004","journal-title":"J. Biomech."},{"key":"ref_26","first-page":"255","article-title":"Wireless insoles to measure ground reaction forces: Step-by-step validity in hopping, walking, and running","volume":"35","author":"Burns","year":"2017","journal-title":"ISBS Proc. Arch."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.measurement.2013.08.020","article-title":"Triaxial joint moment estimation using a wearable three-dimensional gait analysis system","volume":"47","author":"Liu","year":"2014","journal-title":"Measurement"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2597","DOI":"10.1016\/j.jbiomech.2008.05.007","article-title":"Estimating the complete ground reaction forces with pressure insoles in walking","volume":"41","author":"Fong","year":"2008","journal-title":"J. Biomech."},{"key":"ref_29","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_30","doi-asserted-by":"crossref","first-page":"2848","DOI":"10.1016\/j.jbiomech.2010.06.005","article-title":"Determination of joint moments with instrumented force shoes in a variety of tasks","volume":"43","author":"Faber","year":"2010","journal-title":"J. Biomech."},{"key":"ref_31","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_32","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_33","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_34","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_35","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1590\/2446-4740.06817","article-title":"Prediction of 3D ground reaction forces during gait based on accelerometer","volume":"34","author":"Leporace","year":"2018","journal-title":"Res. Biomed. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Karatsidis, A., and Schepers, M. (2016). Estimation of Ground Reaction Forces and Moments During Gait Using Only Inertial Motion Capture. Sensors, 17.","DOI":"10.3390\/s17010075"},{"key":"ref_37","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_38","doi-asserted-by":"crossref","unstructured":"Dorschky, E., Nitschke, M., Martindale, C.F., Bogert, A.J.v.D., Koelewijn, A.D., and Eskofier, B.M. (2020). CNN-Based Estimation of Sagittal Plane Walking and Running Biomechanics From Measured and Simulated Inertial Sensor Data. Front. Bioeng. Biotechnol., 8.","DOI":"10.3389\/fbioe.2020.00604"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/TBME.2020.3006158","article-title":"Multidimensional Ground Reaction Forces and Moments From Wearable Sensor Accelerations via Deep Learning","volume":"68","author":"Johnson","year":"2021","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1249\/MSS.0000000000002562","article-title":"Site-specific Concurrent Validity of the ActiGraph GT9X Link in the Estimation of Activity-related Skeletal Loading","volume":"53","author":"Higgins","year":"2021","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1249\/MSS.0b013e31829ba765","article-title":"Use of Accelerometry to Classify Activity Beneficial to Bone in Premenopausal Women","volume":"45","author":"Stiles","year":"2013","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_42","unstructured":"Denoth, J. (1986). Biomechanics of Running Shoes, Human Kinetics."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1123\/ijsb.7.3.303","article-title":"Relationships between Ground Reaction Force and Tibial Bone Acceleration Parameters","volume":"7","author":"Hennig","year":"1991","journal-title":"Int. J. Sport Biomech."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1123\/jab.9.4.306","article-title":"Use of Ground Reaction Force Parameters in Predicting Peak Tibial Accelerations in Running","volume":"9","author":"Hennig","year":"1993","journal-title":"J. Appl. Biomech."},{"key":"ref_45","first-page":"225","article-title":"Predicting Impact Shock Magnitude: Which Ground Reaction Force Variable Should We Use?","volume":"6","author":"Greenhalgh","year":"2012","journal-title":"Int. J. Sport. Sci. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.gaitpost.2016.02.002","article-title":"Comparison of the correlations between impact loading rates and peak accelerations measured at two different body sites: Intra- and inter-subject analysis","volume":"46","author":"Zhang","year":"2016","journal-title":"Gait Posture"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.jbiomech.2019.01.039","article-title":"Validity and reliability of peak tibial accelerations as real-time measure of impact loading during over-ground rearfoot running at different speeds","volume":"86","author":"Berghe","year":"2019","journal-title":"J. Biomech."},{"key":"ref_48","first-page":"199","article-title":"Predicting Ground Reaction Forces in Sprint Running Using a Shank Mounted Inertial Measurement Unit","volume":"2","author":"Thiel","year":"2018","journal-title":"Proceedings"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1002\/pmrj.12275","article-title":"Outerleys and I. Davis. Tibial Acceleration Measured from Wearable Sensors Is Associated with Loading Rates in Injured Runners","volume":"12","author":"Tenforde","year":"2020","journal-title":"PMR"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.jsams.2017.06.010","article-title":"Use of a tibial accelerometer to measure ground reaction force in running: A reliability and validity comparison with force plates","volume":"21","author":"Raper","year":"2017","journal-title":"J. Sci. Med. Sport"},{"key":"ref_51","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_52","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.jbiomech.2011.12.006","article-title":"Accelerometer counts and raw acceleration output in relation to mechanical loading","volume":"45","author":"Rowlands","year":"2012","journal-title":"J. Biomech."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1113\/jphysiol.1971.sp009595","article-title":"The mechanics of sprint running","volume":"217","author":"Cavagna","year":"1971","journal-title":"J. Physiol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1080\/14763141.2013.811284","article-title":"Validity of an upper-body-mounted accelerometer to measure peak vertical and resultant force during running and change-of-direction tasks","volume":"12","author":"Wundersitz","year":"2013","journal-title":"Sports Biomech."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.jbiomech.2017.07.035","article-title":"The use of a single inertial sensor to estimate 3-dimensional ground reaction force during accelerative running tasks","volume":"61","author":"Gurchiek","year":"2017","journal-title":"J. Biomech."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"e11199","DOI":"10.7717\/peerj.11199","article-title":"Sacral acceleration can predict whole-body kinetics and stride kinematics across running speeds","volume":"9","author":"Alcantara","year":"2021","journal-title":"PeerJ"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Napier, C., Jiang, X., MacLean, C.L., Menon, C., and Hunt, M.A. (2020). The use of a single sacral marker method to approximate the centre of mass trajectory during treadmill running. J. Biomech., 108.","DOI":"10.1016\/j.jbiomech.2020.109886"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.humov.2003.11.002","article-title":"Comparison of kinematic and kinetic methods for computing the vertical motion of the body center of mass during walking","volume":"22","author":"Gard","year":"2004","journal-title":"Hum. Mov. Sci."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.gaitpost.2009.03.001","article-title":"Measurements of vertical displacement in running, a methodological comparison","volume":"30","author":"Gullstrand","year":"2009","journal-title":"Gait Posture"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1123\/jab.24.3.271","article-title":"Comparison between Kinematic and Kinetic Methods for Computing the Vertical Displacement of the Center of Mass during Human Hopping at Different Frequencies","volume":"24","author":"Ranavolo","year":"2008","journal-title":"J. Appl. Biomech."},{"key":"ref_61","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_62","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_63","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1080\/17461391.2022.2102437","article-title":"Mechanical loading prediction through accelerometry data during walking and running","volume":"23","author":"Veras","year":"2022","journal-title":"Eur. J. Sport Sci."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1037438","DOI":"10.3389\/fspor.2022.1037438","article-title":"Predicting vertical ground reaction forces from 3D accelerometery using reservoir computers leads to accurate gait event detection","volume":"4","author":"Bach","year":"2022","journal-title":"Front. Sport. Act. Living"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1123\/pes.15.1.34","article-title":"Measuring Children\u2019s Vertical Ground Reaction Forces with Accelerometry during Walking, Running, and Jumping: The Iowa Bone Development Study","volume":"15","author":"Janz","year":"2003","journal-title":"Pediatr. Exerc. Sci."},{"key":"ref_66","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_67","doi-asserted-by":"crossref","first-page":"e6105","DOI":"10.7717\/peerj.6105","article-title":"The feasibility of predicting ground reaction forces during running from a trunk accelerometry driven mass-spring-damper model","volume":"6","author":"Nedergaard","year":"2018","journal-title":"PeerJ"},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Derie, R., Robberechts, P., Berghe, P.V.D., Gerlo, J., De Clercq, D., Segers, V., and Davis, J. (2020). Tibial Acceleration-Based Prediction of Maximal Vertical Loading Rate During Overground Running: A Machine Learning Approach. Front. Bioeng. Biotechnol., 8.","DOI":"10.3389\/fbioe.2020.00033"},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Sharma, D., Davidson, P., M\u00fcller, P., and Pich\u00e9, R. (2021). Indirect Estimation of Vertical Ground Reaction Force from a Body-Mounted INS\/GPS Using Machine Learning. Sensors, 21.","DOI":"10.3390\/s21041553"},{"key":"ref_70","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_71","doi-asserted-by":"crossref","first-page":"2339","DOI":"10.1038\/s41598-023-29314-4","article-title":"Estimation of gait events and kinetic waveforms with wearable sensors and machine learning when running in an unconstrained environment","volume":"13","author":"Donahue","year":"2023","journal-title":"Sci. Rep."},{"key":"ref_72","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_73","doi-asserted-by":"crossref","unstructured":"Neugebauer, J.M., Hawkins, D.A., and Beckett, L. (2012). Estimating youth locomotion ground reaction forces using an accelerometer-based activity monitor. PLoS ONE, 7.","DOI":"10.1371\/journal.pone.0048182"},{"key":"ref_74","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_75","doi-asserted-by":"crossref","unstructured":"Charry, E., Hu, W., Umer, M., Ronchi, A., and Taylor, S. (2013, January 2\u20135). Study on Estimation of Peak Ground Reaction Forces using Tibial Accelerations in Running. Proceedings of the IEEE 8th International Conference on Intelligent Sensors, Sensor Networks and Information Processing, Melbourne, Australia.","DOI":"10.1109\/ISSNIP.2013.6529804"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1702","DOI":"10.1080\/02640414.2015.1004638","article-title":"Validation of two accelerometers to determine mechanical loading of physical activities in children","volume":"33","author":"Meyer","year":"2015","journal-title":"J. Sports Sci."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1249\/01.mss.0000675908.47355.4d","article-title":"May the force be with you: Acceleration-based estimates of vertical ground reaction forces during running","volume":"52","author":"Kiernan","year":"2020","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_78","unstructured":"Kim, B., and Park, S. (2020). Estimation of 3D GRF during Running from a Single Sacral Measurement Using Artificial Neural Network, Dynamic Walking."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.medengphy.2020.02.002","article-title":"A neural network method to predict task- and step-specific ground reaction force magnitudes from trunk accelerations during running activities","volume":"78","author":"Pogson","year":"2020","journal-title":"Med. Eng. Phys."},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Day, E.M., Alcantara, R.S., McGeehan, M.A., Grabowski, A.M., and Hahn, M.E. (2021). Low-pass filter cutoff frequency affects sacral-mounted inertial measurement unit estimations of peak vertical ground reaction force and contact time during treadmill running. J. Biomech., 119.","DOI":"10.1016\/j.jbiomech.2021.110323"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1123\/jab.2013-0240","article-title":"Standardizing accelerometer-based activity monitor calibration and output reporting","volume":"30","author":"Coolbaugh","year":"2014","journal-title":"J. Appl. Biomech."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1016\/0021-9290(95)00017-C","article-title":"ISB recommendations for standardization in the reporting of kinematic data","volume":"28","author":"Wu","year":"1995","journal-title":"J. Biomech."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1136\/bjsports-2014-094482","article-title":"Davis. Prospective comparison of running injuries between shod and barefoot runners","volume":"50","author":"Altman","year":"2016","journal-title":"Br. J. Sports Med."},{"key":"ref_84","unstructured":"Madgwick, S.O.H., Harrison, A.J.L., and Vaidyanathan, R. (July, January 29). Estimation of IMU and MARG orientation using a gradient descent algorithm. Proceedings of the IEEE International Conference on Rehabilitation Robotics, Zurich, Switzerland."},{"key":"ref_85","unstructured":"Madgwick, S. (2010). An Efficient Orientation Filter for Inertial and Inertial\/Magnetic Sensor Arrays, x-io."},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Ludwig, S., and Burnham, K. (2018, January 12\u201315). Comparison of Euler Estimate using Extended Kalman Filter, Madgwick and Mahony on Quadcopter Flight Data. Proceedings of the International Conference on Unmanned Aircraft Systems, Dallas, TX, USA.","DOI":"10.1109\/ICUAS.2018.8453465"},{"key":"ref_87","unstructured":"Ludwig, S.A., Burnham, K.D., Jim\u00e9nez, A.R., and Touma, P.A. (2018). Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2018, SPIE."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"11933","DOI":"10.3390\/s120911933","article-title":"A Highly Miniaturized, Wireless Inertial Measurement Unit for Characterizing the Dynamics of Pitched Baseballs and Softballs","volume":"12","author":"McGinnis","year":"2012","journal-title":"Sensors"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.gaitpost.2015.10.022","article-title":"Quantifying performance and effects of load carriage during a challenging balancing task using an array of wireless inertial sensors","volume":"43","author":"Cain","year":"2016","journal-title":"Gait Posture"},{"key":"ref_90","unstructured":"Cain, S.M. (2017, January 8\u201311). IMUs (Inertial Measurement Units): Unboxing the black box. Proceedings of the 41st Annual Meeting of the American Society of Biomechanics, Boulder, CO, USA."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.jbiomech.2015.12.019","article-title":"The high frequency component of the vertical ground reaction force is a valid surrogate measure of the impact peak","volume":"49","author":"Blackmore","year":"2016","journal-title":"J. Biomech."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1249\/01.mss.0000183477.75808.92","article-title":"Biomechanical factors associated with tibial stress fracture in female runners","volume":"38","author":"Milner","year":"2006","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1177\/096228029900800204","article-title":"Measuring agreement in method comparison studies","volume":"8","author":"Bland","year":"1999","journal-title":"Stat. Methods Med. Res."},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Carstensen, B., Simpson, J., and Gurrin, L.C. (2008). Statistical Models for Assessing Agreement in Method Comparison Studies with Replicate Measurements. Int. J. Biostat., 4.","DOI":"10.2202\/1557-4679.1107"},{"key":"ref_95","doi-asserted-by":"crossref","unstructured":"Carstensen, B. (2010). Comparing Clinical Measurement Methods: A Practical Guide, John Wiley & Sons. Ltd.","DOI":"10.1002\/9780470683019"},{"key":"ref_96","unstructured":"Carstensen, B., Gurrin, L., Ekstrom, C., Figurski, M., and Package \u2018MethComp\u2019 (2023, August 23). 12 October 2022. Available online: https:\/\/cran.r-project.org\/web\/packages\/MethComp\/MethComp.pdf."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"585809","DOI":"10.3389\/fspor.2021.585809","article-title":"Running Speed Estimation Using Shoe-Worn Inertial Sensors: Direct Integration, Linear, and Personalized Model","volume":"3","author":"Falbriard","year":"2021","journal-title":"Front. Sport. Act. Living"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1016\/j.gaitpost.2011.06.019","article-title":"Ambulatory running speed estimation using an inertial sensor","volume":"34","author":"Yang","year":"2011","journal-title":"Gait Posture"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"4759626","DOI":"10.1155\/2016\/4759626","article-title":"Determine the Foot Strike Pattern Using Inertial Sensors","volume":"2016","author":"Shiang","year":"2016","journal-title":"J. Sensors"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/S0765-1597(02)00122-3","article-title":"Runner\u2019s stride analysis: Comparison of kinematic and kinetic analyses under field conditions","volume":"17","author":"Auvinet","year":"2002","journal-title":"Sci. Sports"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/14763141.2022.2129089","article-title":"The influence of surface and speed on biomechanical external loads obtained from wearable devices in rearfoot strike runners","volume":"10","author":"Miltko","year":"2022","journal-title":"Sports Biomech."},{"key":"ref_102","first-page":"183","article-title":"Assessing Thoracic and Lumbar Spinal Curvature Norm: A Systematic Review","volume":"9","author":"Norasteh","year":"2019","journal-title":"Phys. Treat. Specif. Phys. Ther. J."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0268-0033(95)00068-2","article-title":"Relationship between vertical ground reaction force and speed during walking, slow jogging, and running","volume":"11","author":"Keller","year":"1996","journal-title":"Clin. Biomech."},{"key":"ref_104","unstructured":"United States Geological Survey (2019, June 05). Gravity Anamoly Map of the Continental United States, Available online: https:\/\/mrdata.usgs.gov\/gravity\/map-us.html#home."},{"key":"ref_105","unstructured":"National Geodtic Survey (2019, June 05). NGS Surface Gravity Prediction. National Oceanic and Atmospheric Administration, Available online: https:\/\/www.ngs.noaa.gov\/cgi-bin\/grav_pdx.prl."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1016\/0021-9290(91)90166-K","article-title":"Three-dimensional acceleration of the tibia during walking and running","volume":"24","author":"Lafortune","year":"1991","journal-title":"J. Biomech."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problems","volume":"82","author":"Kalman","year":"1960","journal-title":"Trans. ASME\u2013J. Basic Eng."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1109\/TAC.2008.923738","article-title":"Nonlinear complementary filters on the special orthogonal group","volume":"53","author":"Mahony","year":"2008","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1249\/MSS.0000000000001686","article-title":"Predicting Ground Reaction Force from a Hip-Borne Accelerometer during Load Carriage","volume":"50","author":"Neugebauer","year":"2018","journal-title":"Med. Sci. Sports Exerc."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/21\/8719\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:11:50Z","timestamp":1760130710000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/21\/8719"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,25]]},"references-count":109,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["s23218719"],"URL":"https:\/\/doi.org\/10.3390\/s23218719","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,25]]}}}