Thank you robin 2 for clarification details. I am new to arduino and so I am a little uninformed and uneducated on a lot of these topics. I would like to try and perfect this with the gps, but I feel this project is going to take a lot of time. Which is fine. Curious could this be accomplished with rf transmitters?
I guess would it be possible to make devices with transmitter and receivers built into them, and then when a frequency from one device gets close to another it would light up?
I think that RF transmitters/receivers is probably the only option if the cell phone has been ruled out.
There are a number of RF solutions... low cost 415-433 or 915 MHz transmitters and receivers; WiFi modules, etc. Bluetooth only has a reliable range of about 35 ft., and that would be without interference in the form of prople or buildings between the units. WiFi is an option.. range more like 100-150 ft. One thing in your favour is that because you are looking at two GPS unit outputs when they are close together, the accuracy in absolute position is less important than the relative positions of the units. GPS units in close proximity will all have the same amount and direction of errors that are caused by satellite geometry, geographic terrain, atmospheric conditions, and more.
The first thing to consider is what sort of range you would want to have your units indicate proximity? 15 ft? 50 ft? 100 ft?
A GPS of the type you would find attached to an Arduino is fairly accurate, in best conditions, about +/- 3 ft., and, more typically, +/- 10 ft. Of course, in bad conditions, it could be as bad as +/- a continent or two.
So, let's say you want to go with "light the LED when closer than 50 ft.". The nRF24L01 transceiver modules would likely do the trick, and if you get the ones with the power amp and "stick" antenna, the range will be boosted.
The hardest part, as I mentioned will be to communicate without interference. There are a number of schemes that can be used to separate the signals in time. Time-slots allocated by address is a common way of doing it. It's fairly complex, but not overly difficult to implement.
Again, battery drain will be an important consideration.