Do not Know much about the plans of the FAA regarding the GPS/TCAS baby. But I think that right now it is not on the top of their priority list.
TCAS III was abandonned for 2 reasons : first it proved extremely more difficult to resolve a conflict in the horizontal plane than vertical, both in reality and in software terms. mainly due to the very short time frame in which TCAS operates. .
Secondly current TCAS tracking in azimuth is very poor , and a new version would have necessitated very large changes and very large additional costs. Seen the current price tag of a new TCAS II version 7.0, the project was deemed not cost-efficient.
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I am currently reading the safety study made by the Mitre corporation in 1997 on version 7.0. Interesting to read that their positive risk ratio was derived asuming all pilots will follow all RAs all the time, and that the TCAS does worse when European [airspace] data is included in the model.. (as the system was initially designed for the US airspace model...