ODE parameter estimation through a runner’s model application

The monitoring of sports’ performance has become increasingly popular in the past years. For instance, high precision measurement of runners’ speed, foot pace and heart beat are available among others. Usually, coaches are interested in summary statistics of these data to assess the performance of their runners. However, it is uncommon to find a model that exploits the whole time series. The present report utilizes an ordinary differential equation (ODE) model that captures the runner’s behavior all along his race. This model is based on physical principles, and depends on parameters related to the runner’s physiological characteristics. Based on speed measurements along 200-meter races, this report explores two inference methods specific to the ODE model: the generalized profiling (GP) and the two-step method. Their efficiency will be compared to the standard non-linear least squares (NLS) method. Speed profiles have been sampled at high frequency, and present a correlation structure accounted for with an ARMA process. While the motivation to introduce the GP and the two-step methods are not strictly met for this runner’s model, they present similar estimation quality as the NLS method and emphasize interesting features in terms of model fitting and mis-specification.