I've been considering the limits triangulation for similar applications. I wrote my masters thesis on beamforming, which is a method used to determine direction with a fixed array of sensors. I was working with direction-finding for continuous sounds, like car engines, but that's probably not necessary in this case. Beamforming works quite well with impulse signals, simply by measuring the difference in arrival time at different sensors on the node. Knowing the spatial configuration of the sensors, the direction of origin can be calculated. Make sure all your sensors for a given node aren't in a single plane, and you can even get a 3-d source direction. If you have multiple separated sensor nodes at known locations, triangulation of the source location is trivial. The system works very, very well for determining the location of snipers. So if your child is firing a sniper rifle in a pre-arranged field of sensors, problem solved! Though I make no guarantees about the other problems that might create.
The limit is that any single node can only compute direction of the source, relative to its point of origin. However, since each node has multiple sensors on it, the computations could be performed repeatedly, using each sensor on the node as a point of origin. Four sensors, four directions. In a perfect world, that's more than enough information to triangulate a location in three-space. Attach a device to your child that emits a unique impulse signal every so often, design an appropriate sensor node, and you should be home-free.
But then you get into the fun parts. What kinds of signals? What's the sensor node look like? If you're using EM radiation as your signal, you have to have very precise timing of signal arrival, or a very wide spacing of sensors, or both. Since you want portable, that's probably not practical; difference in arrival time would be under half a nanosecond! I'd consider sound. Much easier to time arrival times that way. Have the child carry a device that occasionally emits an ultrasonic pulse, say a 10 uS 100 kHz pulse every second. High enough no human and most animals won't be able to hear it. You carry an array of microphones with highpass filters on them, wired into an appropriate microprocessor or FPGA to run the beamforming and triangulation calculations.
Now, this all works in theory. In practice, local variations in the speed of sound, sampling rates, etc. are going to introduce error. How much error, I haven't sat down to calculate. I suspect, though, that it's pushing the limits of how well this kind of thing can possibly work. It would, however, be very cheap, probably patent-free, and avoid any problems with EM spectrum licensing.
Not sure if there's audio spectrum licensing...