I have read only a bit about high frequency injection to identify position of motor and it may be used to provide sensor less motor systems.
But I guess you may also use a short ping, to do some of that. I tried to apply a ping on a DC motor and look for the response in speed and some signals as you see below. A PI current control loop operate at 10 kHz. The ping is applied to the current reference, and it is changed each 0.5 ms. You see the response in speed, real current and PWM voltage signal.
I tried to calculate the movement of the shaft, and it is about 0.65 degrees forward and back again. You do also get an audio click response from this, that might be undesirable.
Have you seen any papers or other information on this kind of approach?