Based on the info provided and many assumptions…
(BTW: no idea of venue size, indoors outdoors although ‘room’ does suggest indoors, 20 in a crowd of 100 or 1000+, spacing, walking sitting or both, resolution/accuracy of movement and/or position?, Do you need coordinates or just movement of hand? Do you need to track movements more than one person simultaneously etc etc etc )
You could write an app for their smartphone to use the sensors on board the phone and send that back in realtime over the internet (or local wifi if available)…
(cost of writing the app?)
You could do something similar with a pro mini with and xDoF sensor and an NRF24L01+ with 3xAAs
(circa $10->$20 hardware cost + firmware cost) Simple Bluetooth would work if the venue is not too big.
You could give them relatively powerful IR emitters, which could be tracked by cameras attached to an RPi.
(If at relatively dark you could just use the lights on modern phones, but then everyone could play along ). If indoors both of these should be OK. You would need multiple cameras for 3D movements.
In fact you could potentially just use cheap IR remotes.
Also check out the nintendo wii IR sensors…many cool projects have been done with them.
FYI: Forget tracking wifi or bluetooth by RSSI…usually fails. All the above assumes location coordinates are not required and you are only looking for actual hand movements.
Better suggestions might be possible with more detailed info!
You are not going to get GPS data from phones without an app, and even then the privacy concerns will probably kill the idea... Look on the net for disposable LED art projects. These are powered by a small battery and LED, cost a couple of dollars each maybe less.