Short explanation for the Kalman Filter with a constant Velocity System Model, implemented in Python
Situation covered: You drive with your car in a tunnel and the GPS signal is lost. Now the car has to determine, where it is in the tunnel. The only information it has, is the velocity in driving direction. The x and y component of the velocity (x˙ and y˙) can be calculated from the absolute velocity (revolutions of the wheels) and the heading of the vehicle (yaw rate sensor).
IPython Notebook: nbviewer.ipython.org/github/balzer82/Kalman/blob/master/Kalman-Filter-CV.ipynb?create=1