Disclaimer: I don't know anything about tennis, sorry
Being a physics geek, and thinking this through, I can give you a few suggestions.
The Hawkeye-system will track the real world path of the ball, and then this data goes into the system in order to predict the path of the ball.
The first part tracking the real world path of the ball, and once the positions of image of the ball are registered in the detection process, the next step is triangulating the point of ball in a 3 dimensional coordinate system.
In a simple theoretical world we can ignore air drags, and spins (fluid mechanics), and the the ball will follow a parabolic path as per Newton's laws of motion and gravitation.
I don't know if the Hawkeye system used in tennis would use equations to take into account fluid mechanics, as I mentioned above such as, drag and spin.
If not, Hawkeye's predictive powers are somewhat limited, because It can predict where a ball will go, by extrapolating the existing trajectory of the ball. So it has the ability to make the measurement non-intrusively from long distances for high speed projectiles, therefore the accuracy of the prediction of the ball maybe some small percent off.
That said, due to speed of the projectile (tennis ball) which moves faster at times that our eyes can't judge its exact trajectory, the Hawkeye system is on average more accurate than our perception.