Indoor positioning is a HARD problem. Somethings are easy to do with cheap sensors, some are
not. One approach is SLAM using CV. Yes you are going to have to do the research!
A newish technique on the scene is UWB time-of-flight systems, but I don't think they are cheap
yet and you need 3 or 4 base stations to triangulate. However it looks like they can replace
GPS for indoors with good performance. Any scheme based on signal strength is a non-starter,
note, RF signal strength is very variable and depends on multipath, reflections, polarization.
Ultrasound signal strength has similar issues, but less bad (no polarization to deal with and
time-of-flight is easy).
The UWB systems do time-of-flight on the sub-nanosecond timescale, which is why they are
not ubiqitous and cheap yet (they may become so).
The main issue with indoors is everything reflects RF and sound, and there are numerous obstacles.
Computer vision is complex but it can work well for some applications - particularly autonomous
robotics, and I think this is what you will probably need.
The other way to navigate is to lay a track under the floor to follow - or even paint a stripe on
the floor (works for warehouses and such like).