On a FRC robot, since you don't have access to modify the playing field, you must use encoders/gyros. As I understand this project, you would be allowed to place objects around the perimeter of the field.
Here is how I would do this project...
The player would wear a necklace, wristband, or something of that nature that contains a small IR transmitter. I believe these can be purchased/built in the sub-$20 range. I would also place 3 IR receivers at 3 corners of the court. These shouldn't cost more than $20 a piece as well.
By reading in data seperately from those receivers, you can know the distance from that specific receiver to the transmitter. By using some
basic trigonometry you can figure out where the transmitter is.
Feel free to ask for clarifications.