Are you sure there is no GPS or compass in the base unit? If not, I suppose it would be necessary for it to be given it's initial position by putting the transponder next to it and telling it to zero its position, and the operator would also need to tell it which way it was facing. I'd have thought a second GPS and compass would make it much more use friendly. However, maybe the cost would be prohibitive.
The radio direction finding based approach you're describing would potentially be a faster and more accurate solution, could be used indoors and would be better in many respects - but it would be much harder to get working IMO and would a lot of technological development. What Soloshot already does just needs a neat idea and some readily available technology brought together.