1) AGPS is not local positioning. It is a "speed-up" assist from cellular networks to provide the Almanac (e.g., satellite orbit info) quicker than a GPS receiver can get it from the satellites. All AGPS receivers use the actual GPS satellite signals to calculate the receiver's position. No sats, no position.
2) RTK does not provide a local positioning system. RTK allows a base station receiver, which is in a stable/not-moving site, to observe GPS position calculations over a long period of time and 'averages' the positions to arrive at a highly precise position for itself. It then monitors the real-time positions it calculates and broadcasts a list of error corrections to be applied to the satellite signals to reduce the real-time error, which is constantly changing. Again, no sats, no pos.