Continuous estimation of ground reaction force during long distance running within a fatigue monitoring framework: A Kalman filter-based model-data fusion approach

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