Inertial? no way
You can't a fully inertial system.
The problem is the inicial shoock of the shot will provide way more Gs than current sensors can detect/withstand: so you don't know your speed.
Therefore, you need a laser guidance system so you know where you are. Maybe an hybrid system could be made, with a reduced powder bullet and gyrojet hybrid, laser riding at first and then inertial navigation.
I could see it inside a .50 BMG.. but a 5.56? no way! Maybe an automatic shotgun would be a better option: high caliber, low pressure, slow bullet (but as it is guided, no problem with that).
Still, it would be WAY better to have that for a grenade launcher.