Whether it's outdoor proof or not depends on the housing where you put your electronics.
For position tracking, there are basically 2 ways:
2. Acceleration sensors
For the given distance, a (cheap) GPS solution is not accurate enough (See https://www.sparkfun.com/tutorial/GPSTracking/clamped_edit2-L.jpg, for instance). And it may be too slow for your purpose.
Acceleration sensors also have a simple serial interface, but handling the data to get accurate results is not really easy (However I'm sure that someone has already written a public available software library)
Luckily, for position tracking on a straight line, there's another solution:
3. use a ultrasonic sensor
Maybe there are even better solutions; to evaluate, it would help if you could specify your project more detailed (how exact shall the relative position detection be? Static or dynamic calculation? If dynamic, how fast will the movement be? ...).
It could be worth considering the following alternative:
4. Use a rotary encoder, mount it to a retractable dog leash and hook this to the player's waist. The other end of course must be mounted to a steady pillar. Perhaps this is mechanically tricky, and it limits the mobility of the players, but electrically it's very easy.