If the achievable performances were interesting it would not be a problem to put four per room
Never mind, if there were obstacles, they would still be fixed obstacles
And so with a map of the positions / signal I think we could neutralize the obstacles
Is it known how accurate such a system can be?
I did similar with these Bluetooth iTags:
and they're a heck of a lot cheaper than wifi routers and access points, and don't use up all your mains power sockets or limit your placement options. Battery life was 3-6 months = $2 per year per iTag. I used three or four in each room = $7 per room per year. Accuracy in open space was to within about one metre (horizontally). Main problem was that (usually) one or (sometimes) two of the signals would be attenuated heaps depending on which way I was facing and whether my body was in-between the iTag and the phone. I agree that with fixed obstacles and a map of signal strengths at known positions, you could probably operate in areas that aren't simple open space.
A nice thing was that the BLE2 scan returns RSSI, no need to connect to the devices except for occasionally checking the battery condition (or sounding the alarm so can find the ones that my housemates would helpfully move without telling me).
Another nice thing was the BLE2 scan was detecting lots of other devices besides my poor-man's-beacon iTags, eg, television, speakers, gaming consoles, mobile phones, laptops, remote-control light globes, dad's hearing aid base station, but you had to work out which of those were in a fixed location vs which would move about or even leave entirely.
Sadly I don't have the code any more, after a digital calamity last year during which I discovered my online backup service had lapsed a few months after the payment card expired and warning emails were misfiltered as spam. Spewin! But the math was pretty straightforward, aside from the body-in-the-middle problem.