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Estimation of ground reaction forces in runners has been limited to laboratory environments by means of instrumented treadmills, in-ground force plates and optoelectronic systems. Recent advances in estimation techniques using wearable sensors for kinematic analysis and sports performance could enable estimation outside the laboratory. This paper proposes a state-input-parameter estimation framework to continuously estimate the vertical ground reaction force waveform during running. By modeling a runner as a single degree of freedom mass-spring-damper with acceleration measurements at the sacrum a state-space formulation can be applied using Newtonian methods. A dual-Kalman filter is employed to estimate the unmeasured system input which feeds through to an unscented Kalman filter to estimate system dynamics and unknown model parameters (e.g. spring stiffness). For validation, 14 subjects performed three one-minute running trials at three different speeds (self-selected slow, comfortable, and fast) on a pressure-sensor-instrumented treadmill. The estimated vertical ground reaction force waveform parameters; peak vertical ground reaction force (RMSE=6.1-7.2%,ρ=0.95-0.97), vertical impulse (RMSE=8.5-13.0%,ρ=0.50-0.60), loading rate (RMSE=24.6-39.4%,ρ=0.85-0.93), and cadence RMSE<1%,ρ=1.00 were compared against the instrumented treadmill measurements. The proposed state-input-parameter estimation framework could monitor personalized vertical ground reaction force metrics for potential biofeedback applications. The feedback mechanism could provide information about the vertical ground reaction force characteristics to the runner as they are running to provide knowledge of both desirable and undesirable loading characteristics experienced., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

The purpose of this investigation was to determine the feasibility of using a single inertial measurement unit (IMU) placed on the sacrum to estimate 3-dimensional ground reaction force (F) during linear acceleration and change of direction tasks. Force plate measurements of F and estimates from the proposed IMU method were collected while subjects (n=15) performed a standing sprint start (SS) and a 45° change of direction task (COD). Error in the IMU estimate of step-averaged component and resultant F was quantified by comparison to estimates from the force plate using Bland-Altman 95% limits of agreement (LOA), root mean square error (RMSE), Pearson's product-moment correlation coefficient (r), and the effect size (ES) of the differences between the two systems. RMSE of the IMU estimate of step-average F ranged from 37.70 N to 77.05 N with ES between 0.04 and 0.47 for SS while for COD, RMSE was between 54.19 N to 182.92 N with ES between 0.08 and 1.69. Correlation coefficients between the IMU and force plate measurements were significant (p≤0.05) for all values (r=0.53 to 0.95) except the medio-lateral component of step-average F. The average angular error in the IMU estimate of the orientation of step-average F was ≤10° for all tasks. The results of this study suggest the proposed IMU method may be used to estimate sagittal plane components and magnitude of step-average F during a linear standing sprint start as well as the vertical component and magnitude of step-average F during a 45° change of direction task., (Copyright © 2017 Elsevier Ltd. All rights reserved.)