guessing distance by FM signal strength

I'm not expecting any form of obstruction between the objects.

The problems are not obstacles in between, but things that cause reflections which can be anything.
You are not the first to think of this idea, what are the odds that you will be the first to make it work.

The closest they come is in this app note attached.

appnote_016_sna_ti_locationing.pdf (295 KB)