From a long and very good article in Vanity Fair about a Brazillian mid-air collision last year, when two aircraft coming from opposite directions were given the same altitude and heading. The autopilots were so accurate that the two planes hit each other dead on in the open skies over the vast Amazonian rain forest: Excerpt:
"Navigational precision poses dangers not immediately apparent. In the Legacy, it was based on three systems. The first was an ultra-accurate altimeter, capable of measuring the atmosphere with such finesse that at Flight Level 370 it could distinguish the Legacy's altitude within perhaps five feet. The second was almost as accurate. It was the airplane's satellite-based G.P.S. receiver, a positioning system that kept track of the airplane's geographic location within a distance of half of its wingspan, and that, linked to a navigational database, defined the assigned airway with equal precision. The third was an autopilot that flew better than its human masters, and, however mindlessly, worked with the altimeter and G.P.S. to keep the airplane spot-on. Such capability is relatively new. Until recently, head-on airplanes mistakenly assigned the same altitude and route by Air Traffic Control would almost certainly have passed some distance apart, due to the navigation slop inherent in their systems. But this is no longer true. The problem for the Legacy was that the Boeing coming at them on the same assigned flight path had equipment that was every bit as precise."