For this project, as well as others like mine (I'll mention after), I would also consider Low Energy Bluetooth or BTLE.
It would be using radio signals like you said.
I would like to see how I, or a cat, or anyone spends there time. Working from home I spend most my day in the house and mostly at the desk or behind the computer screen. But it would be interesting to collect, analyze and visualize this information.
1) Just set up a few fixed-point broadcasting "towers" with the Arduino on the user as a receiver, recording tower_ID and tower_amplitude and simply triangulate.
2) Set up the user / tennis player / cat as the broadcaster and each tower as a receiver.
Each can be ideal for different situations. Consider how long the User must wear the device, how heavy it can be and thus how much power it can carry.
^ My bet would be that method 1 would require more sophistication and thus a larger arduino / shield / power combination to be worn on the User (Tennis player) / Person (Me) / Cat (not me).
^^ Not so good for tennis or action sports, but not a big deal for me lounging around the house in my sweat pants ([See Loss Of Regimen in TheOatMeal blog about working from home post] for lolz)
With the second method you could use a cheap BTLE transmitter that is lightweight (most the weight of these are made up of the watch battery used to power them) about the size and weight of a 3 stacked quarters.
The receiver towers could then be designed with power systems that don't require the cost of reduced weight.
The Second method would, however, require a little extra post data munging since you would need to reconcile data from multiple source inputs rather than method 1's use of a single source with multiple inputs.
I am still digging around with the project myself having just started researching today and won't get around to designing later this month.
Please feel free to contact me with any ideas, suggestions or questions
My Personal Website or LinkedIn
My website / blog is way over due for a make-over and update of past and current projects. But in the coming months I will post projects such as the Brain-Computer-Interface I used to control a synthesizer with, a tactile interface which gave users texture feedback from interacting with digital objects (such as feeling a smooth surface in a picture of granite or a rigid or bumpy surface from accord pictures or programmed game objects with meta data read by the Arduino controlled feedback system build into and around a mouse)