Reconstructing ground reaction force curves from a single accelerometer using functional principal components

The gold standard for estimating jump height and peak power in the countermovement jump (CMJ) relies on force plates measuring the vertical ground reaction force (vGRF), a waveform that captures movement strategy. However, this equipment is impractical in the field. Instead, this study reconstructs vGRF waveforms from one lower-back accelerometer using a dual functional principal component analysis (FPCA) representation. Four representations (raw, smoothed, B-spline, FPC) were mapped to the vGRF with an MLP, and the raw and smoothed signals also with a transformer, across 663 jumps from 67 participants. The FPC-based MLP reconstructed the waveform with R² of 0.96 and 0.98, respectively, with and without arm swing. The features a practitioner reads from the curve survived the reconstruction: countermovement depth to R² = 0.91, peak force to 0.87, the braking-to-propulsion transition force to 0.91 and the propulsive impulse to 0.82. Deriving performance metrics from the reconstructed vGRF tested fidelity more stringently than R² alone. Jump-height and peak-power errors were 4.0 cm and 3.7 W·kg^-1, rising to 6.1 cm and 5.6 W·kg^-1, indicating the reconstructed waveform can serve as a reasonable facsimile. The lower-dimensional FPC mappings reduced the model from 128K to around 4K parameters, while improving accuracy.