The issue being, whether they would have the same error as each other in positional accuracy and hence would be very accurate in relative position to each other (e.g. to measure bank angle?)
Some research has been done to see if this is feasible. I remember
NLR did something in this area. To get accurate results you need to have the antenna's on separate locations (wingtips), but you probably will have to do the data processing in one unit, making sure that you use the same satellites for calculating the positions of both antennas. And by looking at phase shifts, you can probably derive the roll rate.
And, by the way, I think the second issue also has implications for ADS-B as a proximity warning, particularly for light aircraft, if that ever comes about, as ADS-B seems to be a sort of Flarm-like concept AIUI.]
It has indeed. Since ADS-B does not restrict the algorithms used inside the GPS unit, different errors exist between different receivers. But even if a same GPS unit would be used in the other aircraft, the position errors would differ. As Urs explains, this can happen due to multipath (reflection of the signal), or the use of different satellites (i.e. satellites shielded by the wing in a turn).
Among other things, ADS-B sends quality indicators which indicate the accuracy and the integrity of the position report. They can be combined into a containment radius. This containment radius is usually governed by the integrity bound. That is the size that an error can grow undetected by the RAIM algorithm due to a single faulty satellite. A typical position error is in the order of 10 feet, but the size of the undetectable error due to a faulty satellite can grow to much more than that. A typical containment bound is 0.2 NM. Note that the RAIM algorithm is not standardized either, so different GPS receivers will give different containment bounds.
For proximity warning the typical containment bound is good enough, for collision avoidance it might be better to look at the accuracy instead of the integrity, and assume that the satellites are performing well.
Regards,
ATCast