A Multivariate Polynomial Regression to Reconstruct Ground Contact and Flight Times Based on a Sine Wave Model for Vertical Ground Reaction Force and Measured Effective Timings

Effective contact ( [Formula: see text] ) and flight ( [Formula: see text] ) times, instead of ground contact ( [Formula: see text] ) and flight ( [Formula: see text] ) times, are usually collected outside the laboratory using inertial sensors. Unfortunately, [Formula: see text] and [Formula: see text] cannot be related to [Formula: see text] and [Formula: see text] because the exact shape of vertical ground reaction force is unknown. However, using a sine wave approximation for vertical force, [Formula: see text] and [Formula: see text] as well as [Formula: see text] and [Formula: see text] could be related. Indeed, under this approximation, a transcendental equation was obtained and solved numerically over a [Formula: see text] 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 [Formula: see text] values. Then, reconstructed [Formula: see text] (using the model) was compared to corresponding experimental ground truth. A systematic bias of 35 ms was depicted, demonstrating that ground truth [Formula: see text] values were larger than reconstructed ones. Nonetheless, error in the reconstruction of [Formula: see text] from [Formula: see text] 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 [Formula: see text] and [Formula: see text] in real time, which would allow coaches and practitioners to better evaluate running performance and to prevent running-related injuries.