But work in the field of full automation is well underway
In terms what is feasible in the near future in passenger aircraft it is not an unmanned aircraft but SOP - single pilot operations. In other words an aircraft cockpit with single pilot only. There would be another "virtual" pilot on the ground. NASA is actually in the midst of extensive studies/simulations of this very topic. I work at NASA Ames and this is the hottest topic pursued at the moment in the aeronautics division of NASA. Air Rabbit is correct - a fully autonomous passenger aircraft is not yet on anybody's drawing boards, but SOP is very much on the drawing boards.