I have found that GPS signal has no way of interpreting orientation.
Strange. Mine has no problem at all telling which way I am going. Strolling around the yard, maybe. At any decent speed, it works fine. It, of course, determines direction from adjacent location data, so if the locations are very close together (walking speed), direction is not going to be accurate. If the adjacent locations are far enough apart, direction IS meaningful.
But, in order for a robot to follow a person, using GPS, both the robot and the person need GPS units AND the person needs to communication his/her location to the robot. Given the typical accuracy of GPS, using two different units for following would work fine, if you don't need the robot to stay real close and you don't mind running around the yard at 30 mph.