the fact you are indoors does not nullify gps.
you could put transceivers on the edges of the floor, and interpolate the results. Previous to gps, these systems were in use in the U.S.: Omega and Loran. They worked basically the same: Each system has a master transmitter, and a minimum of two slaves. The master transmits a signal. When a slave receives the master signal, it then transmits its signal on a different frequency. By bouncing the received signals off each other relative to the time of arrival at the ship, you can interpolate your posititon. The difference between Loran and Omega, is for the Omega system, we would get charts overprinted in their frequencies for the area we would be operating in. The receiver would give us numbers on the slave channels, and we would chart our positions using the overprinted charts. Loran, however, gave us a readout of lat and long directly (newer system). Problem: worked great during the day, gave us a nice little triangle for a fix, and as dusk approached the triangles would get bigger and bigger until we could tell we were somewhere in the Caribbean... now, these transmitters covered thousands of miles. You are only covering hundreds of feet. Radio waves (and light) travel at 1 foot/nsec. That means with 100 feet differential, you'd have signals 100 nsec, or .1usec (yes, that's a tenth of a microsecond) apart. Can you measure that accurately? You'll get some big triangles. I suggest for this type of system on this scale sound would be a better selection.
gps? gps is only accurate to 10 feet on a good day. Of course, all receivers would have the same error, so if you have a receiver at your central location, then all fixes would be relative to that central location.