[andybak]

Is there any sensor or combination of sensors in modern phones capable of doing this?

I suppose the obvious one is to use the front-facing camera and some external markers but that might be very CPU-intensive.

[yincrash]

Google Tango is attempting to accomplish it by using the camera sensor to measure positional changes.[1] They showed it off at Google I/O, but it was a bit eclipsed by Cardboard (probably to the chagrin of the Tango team).

[1] https://www.google.com/atap/projecttango/

[efraim]

Project Tango doesn't just use a camera to track position, it uses structured light - like the first kinect - with an infrared projector and camera to build up a 3D model of the environment.

https://www.ifixit.com/Teardown/Project+Tango+Teardown/23835