A Multivariate Polynomial Regression to Reconstruct Ground Contact and Flight Times Based on a Sine Wave Model for...

Effective contact ( $$ ) and flight ( $$ ) times, instead of ground contact ( $$ ) and flight ( $$ ) times, are usually collected outside the laboratory using inertial sensors. Unfortunately, $$ and $$ cannot be related to $$ and $$ because the exact shape of vertical ground reaction force is unknown. However, using a sine wave approximation for vertical force, $$ and $$ as well as $$ and $$ could be related. Indeed, under this approximation, a transcendental equation was obtained and solved numerically over a $$ grid. Then, a multivariate polynomial regression was applied to the numerical outcome. In order to reach a root-mean-square error of 0.5 ms, the final model was given by an eighth-order polynomial. As a direct application, this model was applied to experimentally measured $$ values. Then, reconstructed $$ (using the model) was compared to corresponding experimental ground truth. A systematic bias of 35 ms was depicted, demonstrating that ground truth $$ values were larger than reconstructed ones. Nonetheless, error in the reconstruction of $$ from $$ was coming from the sine wave approximation, while the polynomial regression did not introduce further error. The presented model could be added to algorithms within sports watches to provide robust estimations of $$ and $$ in real time, which would allow coaches and practitioners to better evaluate running performance and to prevent running-related injuries.