This doesn't work very good with the kind of sensor in the article

Yes, there is no state and state transition matrix, really.

Kalman filters are good where you have a system with a state, and an estimate of the state, and you act on the system, and then you measure the outcome, repeatedly.

Acting on the system and propagating your estimate forward "one step" increases the uncertainty of your estimate, and measuring decreases the uncertainty of your estimate.