# Discretization of continuous model with white noise to use Kalman filter later

I have this system which describes dynamics of a car in 2D space. The dynamics are governed by Newton's law g(t) = ma(t). The final task is to use Kalman filter on discretized system to estimate it's position and velocity. The measurements are based on GPS signal with some covariance.

Unfortunately, I already got stucked at the beginning. I dont know how to incorporate the G matrix with w and e into discretization. Based on what I've learned, it should meant process and measurement noise. Therefore it doesnt effect the dynamics of the system itself and I shouldnt count it during the discretization. Am I right? However based on the assignment, I should somehow edit w and e for the discretized model. In that case, why Gc dissappears? Of course, then the different time steps confuse me as well :(

In order to achieve this result, can I just use ss function in MATLAB to create system and then use c2d function to discretize it? I just look at this already two days and since I'm just overall confused about the course of actions, I havent moved a bit.

Description of the problem

If I could ask you for some advice how to proceed I would really appreciate a lot!! Thanks in advance