This guy, Andreas from Germany, that have made this amazing motor drive and video do also have a blog. I tried to contact him, but I am not sure if this is successful. In comments to video and in his blog, there is some more information. There is a technique called "Frequency Injection", and ads some additional frequency to the motor voltage and look for the result in the measured currents to the motor. In this way the position of the rotor can be detected when the rotor do not turn. Andreas confirmed, that he use frequency injection.
In my study of these controllers I have seen these other two videos, that explain some of the concepts:
https://www.youtube.com/watch?v=cdiZUszYLiA
and
https://www.youtube.com/watch?v=icdiKL90E3U
The microcontroller chosen by Andreas is from the STM32 family, and it make me think, that this kind of controller might be a good choice for this kind of motor applications, and the cost of them are low too.
Many years ago I did study engineering, and at that time observers and Kalman filters were rather new methods for control of systems. It is however powerful concepts. I remember, that some concepts included to add some noise in the control signal in order to observe the systems reaction, and in this way you were better able to calculate the state and the dynamics of a system.