Earlier quoted context omitted.
Maybe add beeps and use them like a sonar to refine distance measurement?
5m room size / speed of sound in air = around 15ms. Unless the amount of variation in latency in the phone's speaker + microphones is much less than that -- which I suspect it isn't -- that wouldn't be particularly accurate either. (Even that aside, it's going to be rather non-trivial to get anything useful at all with a non-directional speaker in an enclosed room with several other walls, ceiling, floor, and other o…
I think you are right about the likely cluttered response in a realistic room being hard to analyse into something useful.