Improve Smartphone GPS with external RTK - will a simple antenna work?
What you seem to be talking about is called "WAAS" which is a satellite-based correction service that the GPS receiver can receive in parallel with the GPS satellite positioning codes. This signal is used to improve the accuracy of the received code signal. It can get down to 1m accuracy under the right conditions.

Another approach is called "DGPS" or differential GPS. This uses a remote antenna to provide a 'WAAS-like' function for a nearby, mobile GPS. Many chipsets support this, although the functionality seems to be somewhat lightly documented or mostly undocumented. I have never seen this in reference to a smartphone GPS, only on GPS modules in embedded devices -- this is data that the GPS chipset needs to take into account, and can't be utilized well without access to the raw GPS data (not NMEA) which is not readily accessible in most units.

Neither of these methods has anything to do with RTK, except that an RTK system may take advantage of them as part of its acquisition process.

Related Stack Overflow thread: https://stackoverflow.com/questions/9873350/dgps-corrections-on-android

Information on pushing DGPS data into the SiRF chipset: http://usglobalsat.com/downloads/SiRF_Binary_Protocol.pdf