Rnp Saaar = Rnp Ar Apch
The RNP SAAAR Approaches are an FAA invention that have been rolled out in the US (70 approaches), Canada (24 airports), China (3 airports), NZ (1 airport?), Australia(15 airports), Ecuador (1 airport?) and Mexico (1 airport?), over the past 5 years. (Actually it all started in Juneau, Alaska, back in the nineties but it was called a 'special' then)
ICAO adopted the SAAAR idea and re-named it RNP AR APCH when it introduced the PBN Concept last year. Basically, RNP AR Approaches allow fixed radius turns all along the approach/missed approach, short finals (around 1 NM) and 0.1NM track-keeping accuracy.
Quite a few of the so-called RNP SAAAR approaches published today offer little more than the standard 0.3 NM RNP approach although some can be quite sporting (Lhasa, Quito and Queenstown for example)
The problem at the moment is getting approval - the carrier has to demonstrate that the procedure can be flown safely under a range of normal and non-normal conditions and that there are adequate contingency procedures to extract the aircraft in the event of equipment failure. This requires quite a lot of input from the manufacturer and for this reason, most SAAAR approaches are currently only flown by one or two carriers at each airport. (Certain versions of the B737NG and A-320 were the first to get approval - I think that versions of A-330, B757 and B767 are expected to be approved this year)
There are no datalink requirements for RNP AR APCH and I can't see performance getting better than 0.1Nm anytime soon - Galileo or no Galileo.