Radio signals in a room act just like sound in a concert hall: bouncing off walls and objects, they create a unique pattern — a silent melody for every location. Your phone, like a keen ear, catches this melody amid noise and distortion. It remembers which chord matches the corner of the couch, and which one fits the doorway.
The system is so sensitive it detects breathing: the rise of your chest slightly changes the reflection pattern, and this is already used for sleep monitoring. From there, it's a short step to navigating subways and factories without satellites.
Reflecting off your body, the signal even detects breathing — the rise of your chest shifts the invisible note just a little. This is already used for sleep monitoring without cameras or sensors.
In the movie 'The Dark Knight', Batman turned all of Gotham's phones into a massive tracking system. A similar approach, but for peaceful navigation, is already being explored in labs.