>Can they detect relative movement on the order of 1cm or less?
The short answer is no, largely due to localised ionospheric conditions. The longer answer is yes, GNSS systems can be enhanced in accuracy using RTK [0][1]. This allows for precision on the order of 1cm, but requires a (rather expensive) fixed position base station to provide corrections. Surveyors, precision ag, and other large machine control (think dozers, graders, etc) have used this technique for precision positioning for the past decade or so.
I do recall reading that upcoming GPS satellites add a second civilian frequency, which I believe will enable these sort of ionospheric corrections to be done more easily and inexpensively.
I don't know quite enough about the technical details to be sure, but RTK can defintiely go over IP networks with NTRIP and other protocols. The biggest limitation with RTK is that the corrections are limited to 10-15 miles of the base/reference station (more is possible, generally with less accuracy), since ionospheric conditions vary enough to make the corrections highly location dependant.
The antenna systems on RTK rovers (the devices receiving corrections, which also receive the GPS satellite signals) aren't huge, but I'm not sure if they could be reduced in size enough to fit in a smartphone.
The short answer is no, largely due to localised ionospheric conditions. The longer answer is yes, GNSS systems can be enhanced in accuracy using RTK [0][1]. This allows for precision on the order of 1cm, but requires a (rather expensive) fixed position base station to provide corrections. Surveyors, precision ag, and other large machine control (think dozers, graders, etc) have used this technique for precision positioning for the past decade or so.
I do recall reading that upcoming GPS satellites add a second civilian frequency, which I believe will enable these sort of ionospheric corrections to be done more easily and inexpensively.
[0] http://www.navipedia.net/index.php/RTK_Fundamentals
[1] https://en.wikipedia.org/wiki/Real_Time_Kinematic