Check out Qubulus. Their indoor positioning API uses an RF fingerprinting method for Android devices. Right now, your software-only options are limited for iOS. Best tip there is to wait for iPhone 5. I'm not familiar with options for Blackberry.
A full list of indoor positioning technology providers is here: http://bit.ly/indoornavigation
You might also gain some insight from reading "Why Indoor Navigation is So Hard". The O'Reilly article mentions the Cisco MSE option, which is likely a better fit for your needs than a GPS repeater.
We actually did a lot of research on implementing a system like this for our elderly customers. The problem with any tag based system is the same problem with any PERS system (I've fallen etc...). The problem is most people just won't wear the tags / monitoring bracelets. The closest thing we came up that might work would be having the family sew small tags into all their pants, or using the small space in a nike shoe where they keep their Nike+ hardware to store a xcvr. We also looked into using watches, but what we needed were nice metal watches not the plastic timex style ones that were available with xcvrs in them. Oh and there was talk of planting something in walkers and canes, if someone needs that to get around you could do it I guess.
There were plenty of meetings with talk about "social contracts" between the eldery caree and the caregiver where they would agree to use the tags but it was BS because the elderly were just not interested.
In the end we settled on a more complicated version of what you describe. Motion sensors throughout the house that communicate to our backend servers. There we process daily living patterns to determine if anything might be up. Has no one opened the fridge at 8AM, bathroom not used in last 4 hours but should have been, etc. Combining multiple sources seemed the way to go.
However that wasn't even the final solution for our customers. The expense of installing and configuring all those sensors is a pain in the... So our final solution is a touch screen system that the elderly use to check in on every day. The software and UI was designed specifically for an elderly user, and has things to check on medicine usage, are they ok. But it also implements a family section as well, with pictures, games, activities, video chat, email, web and a lot more. All designed for elederly non computer users.
This ended up engaging the elderly person a lot more, and we were able to take all of that information into our backend where the family or pro caregiver could see how they were doing. If someone fell we might not know right away but we'd know when they missed their next checkin. So not exactly what you're asking for but I thought I'd share our experience and see if it helped you out.
Best Answer
You probably want to check out OpenBeacon, which implements this sort of tracking using an 'Active RFID' tag. A bonus of this is that it already includes the 2-way radio you'll need to instruct tags to blink.
Triangulation is done by positioning a large number of basestations around the venue, and having tags transmit pulses at varying amplitudes. By examining which set of nodes can be reached at each amplitude, the system can narrow down where the user is likely to be. They're a little vague on what sort of accuracy the system can claim, though, or how it deals with interference due to things like obstructing walls.