Gaussian Processes for Analyzing Positioned Trajectories in Sports

TL;DR

This paper introduces a grey-box Gaussian process modeling approach to analyze forces and velocity in cross country skiing, combining physics-based models with data-driven methods for improved uncertainty reduction.

Contribution

It presents a novel grey-box modeling framework that integrates kinetic motion models with Gaussian process regression for sports trajectory analysis.

Findings

Grey-box approach reduces predictive uncertainty by 30-40%.

Models effectively analyze forces and velocities in skiing races.

Applicable to scenarios with positioned trajectories and kinetic data.

Abstract

Kernel-based machine learning approaches are gaining increasing interest for exploring and modeling large dataset in recent years. Gaussian process (GP) is one example of such kernel-based approaches, which can provide very good performance for nonlinear modeling problems. In this work, we first propose a grey-box modeling approach to analyze the forces in cross country skiing races. To be more precise, a disciplined set of kinetic motion model formulae is combined with data-driven Gaussian process regression model, which accounts for everything unknown in the system. Then, a modeling approach is proposed to analyze the kinetic flow of both individual and clusters of skiers. The proposed approaches can be generally applied to use cases where positioned trajectories and kinetic measurements are available. The proposed approaches are evaluated using data collected from the Falun Nordic World Ski Championships 2015, in particular the Men's cross country $4\times10$ km relay. Forces during the cross country skiing races are analyzed and compared. Velocity models for skiers at different competition stages are also evaluated. Finally, the comparisons between the grey-box and black-box approach are carried out, where the grey-box approach can reduce the predictive uncertainty by $30\%$ to $40\%$.