Publication

ODE parameter estimation through a runner's model application

2016
Student Projects

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/5e3059b6-b2d7-4c64-9480-6b26dbb04e34

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2016
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/5e3059b6-b2d7-4c64-9480-6b26dbb04e34

About this result

Related concepts (32)

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Runge–Kutta methods

In numerical analysis, the Runge–Kutta methods (ˈrʊŋəˈkʊtɑː ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".

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ODE parameter estimation through a runner's model application

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