I do hope self-driving software works out a better system, before it becomes common place. Autopilot has been incorporating GPS in aviation for decades, and it's still surprisingly common to have major problems when a loss of GPS occurs.

The Phenom 300 jet can't fly straight without a valid GPS signal: https://news.ycombinator.com/item?id=12519629

Every swept-wing jet has a tendancy to enter a positive feedback loop of rolling and yawing, called a dutch roll, when flying at altitude, so even when not using autopilot, an active system is needed to fly straight and level. If the Phenom 300 doesn't have a valid GPS signal, that system fails.