Creating "local gps" system

I am talking about 3-10 meters area

I am thinking there is no way you will be able to do this. Work out the speed of light. 3 10-8 meters / second and you will see how accurate you will have to be. It's something that you can't just throw together. Most systems working over that range (like zigbee) use signal strength rather than flight time. The TI zigbee chip set has built in signal strength detectors to do just this but you need more than the minimum to do it with any reliability. The zigbee demos I have seen use at least 6 and possibly more.
If you want a ready made system look at the zigbee development kits, these usually come with 6 transmitters, but it is not cheap.