Rifle bullets are supersonic, and consequently give off a small sonic boom. Audible, so my long-ago military training class instructor noted, as a snap as it passes by. It follows that data from a sufficent microphone array beside/behind (and, obviously, preferably also in front of) the target could be compared to infer the track of the bullet. The further apart the microphones roughly along the bullet's path, the greater the potential resolution capability--but you would need to know the geometry of the microphone array, if it wasn't a constant. So you could deploy microphones by mortar shell if you needed them widely spaced, but that would leave you with operational problems figuring out where the mikes actually fell. That might be solvable by deliberately firing a known shot or two over the array, perhaps . . . but if you had a squad of troops and each one had a mike with some kind of position measurement transponder . . . After that, it would be a matter of operating a Kalman filter, perhaps, to infer the flight paths of incoming rifle shots. Computer processing power would be, at this late date, the least of the problems, given that GPS boxes are under $1000 and we're talking about somewhat similar analysis.
It seems like it would be easy to fool the system with decoy gunshots.