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Analysis of Football Player’s Motion in View of Fractional Calculus

Couceiro, M. Couceiro ; Clemente, F.M.C. ; Martins, F.

Central European Journal of Physics Vol. 11, Nº 6, pp. 714 - 723, October, 2013.

ISSN (print): 1895-1082
ISSN (online): 1644-3608

Journal Impact Factor: 0,909 (in 2011)

Digital Object Identifier: 10.2478/s11534-013-0258-5

Abstract
Accurately retrieving the position of football players over time may lay the foundations for a whole series of
possible new performance metrics for coaches and assistants. Despite the recent developments of automatic
tracking systems, the misclassification problem (i.e., misleading a given player by another) still exists and
requires human operators as final evaluators. This paper proposes an adaptive fractional calculus (FC)
approach to improve the accuracy of tracking methods by estimating the position of players based on their
trajectory so far. One half-time of an official football match was used to evaluate the accuracy of the
proposed approach under different sampling periods of 250, 500 and 1000 ms. Moreover, the performance
of the FC approach was compared with position-based and velocity-based methods. The experimental
evaluation shows that the FC method presents a high classification accuracy for small sampling periods.
Such results suggest that fractional dynamics may fit the trajectory of football players, thus being useful
to increase the autonomy of tracking systems.
PACS (2008): 01.80.+b, 45.40.-f, 02.70.-c, 02.60.-x, 05.45.Tp
Keywords: Football • Prediction Methods • Fractional Calculus • Fractional Dynamics