Signal triangulation
About RF:

The idea is to cast let's say 100Mhz signal and measure phase shift between received signals in different points. Then you'll be able to calculate the location.

Measuring time difference directly could be tricky, as you will need 0.1ns or better accuracy (1ns = 30cm in air).



Piezo-emitters are very capable going into sub-Mhz sound range. Nearly any mic(probably except coal one) can receive 50-100Khz sound with proper amplification. Safety is usually not a problem as long as you are under-1W range, and I doubt you would need more than 0.01 :-)



RF way is way harder to implement but I belive more reliable.