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\subsubsection{Extraction of data}  For our experiments we used only data during a restricted period of several minutes beginning at arbitrary time of the play. Computationnaly we defined a trajectory as a set of ordered x and y-axis positions and accelerations regularly distributed in time.   \verb|class trajectory:    def __init__(self):  """  initialization of a trajectory 
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self.ypred = 0.  self.accxpred = 0.   self.accypred = 0.|    Furthermore we will handle a set of synchronized trajectories. This synchronization is highly important since we will used it when we will approximate the joint probability distribution of positions or accelerations of two players.  Data are read and extracted with a frequency of 25 Hz which correspond to the best frequency we could have if we were extracting directly from the videos of the soccer match. As each players is equipped with several sensor we combine their data to have one and only one trajectory per player or ball.