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This is an excellent use of the Kalman Filter. It can estimate the position and velocity of the balls, predict where they will be in the future, and give you a confidence interval of how certain the estimates are.
As for which detection is which track, that is called track association. You should be able to get away with something simple like the Hungarian Algorithm and the distance from the Kalman Filter's prediction. The methods can become amazingly complicated though, as you add more constraints.
