Here we have a GPS and a Acceleration Measurement, which have to be fused optimally via the Kalman Filter
Second example is the same dynamic model but this time you measure the position as well as the acceleration. Both values have to be fused together with the Kalman Filter. Situation covered: You have an acceleration sensor (in 2D: x¨ and y¨) and a Position Sensor (e.g. GPS) and try to calculate velocity (x˙ and y˙) as well as position (x and y) of a person holding a smartphone in his/her hand.
IPython Notebook: nbviewer.ipython.org/github/balzer82/Kalman/blob/master/Kalman-Filter-CA-2.ipynb?create=1