What you are trying to do is known as system identification in the academic literature. Sys Id is a method used to identify the parameters of dynamical systems models from trajectory data.
Once you have a good model fitted to the data, you can then predict the future trajectory of the ball (see also @el_pazzu's answer for using a Kalman filter although this might be tricky with your non-linear system).
Your system is non-linear due to the bouncing behaviour so you will have to set up a non-linear optimization problem and try to solve it for the parameters of your model.
The simplest method of system identification is the single-shooting method which involves simulating an entire trajectory and then comparing it to the outputs from the true system.
This is the prediction error method, which usually involves minimizing the squared-errors between the output trajectory predicted by the model and the data.
Hope that helps. There are many resources online to do this. There are some curated tutorials here:
Also, MATLAB software has a comprehensive set of tools to help you do it.
But I would try solving it using scipy.optimize first. If that doesn't work you may need to consider more advanced non-linear optimization algorithms (see for example, GEKKO, CasADi, Pyomo
Hope that helps. Good luck, it's a very interesting problem...