I think I also understood how HFI works now, or at least one method.
Salient motors have a different inductance on q axis (Lq) and d axis (Ld).
When you measure the inductance and spin the motor, the inductance goes higher when aligned with q axis and lower with d axis.
HFI injects a high frequency square wave, basically you add a voltage to the dq voltages before the SVPWM on one PWM cycle, and substract it on the alternate cycle.
Then you calculate the dq currents difference between the highs and lows.
This let’s you calculate the inductance as we discussed here.
Once you know the inductance, you can derive the angle. For example
if Lq is 300 uH and Lq is 250 uH, and I measure 275 uH, I am half way.
The less salient the motor is, the worse this will work.
So with this SimpleFOC would be able to measure the inductance.
But I think for that it should be interrupt based as I mentionned here.
[EDIT] I might be missing some details about inductance measurement and converting it to an angle, I will update when I know more.