Best heading sensor solution for outdoor fast moving robot

I am building an outdoor robot with differential drive. It will basically be interactive with an operator but must have autonomous heading changes triggered by a button push. So the robot will be travelling at approx 10mph....the operator will hit a remote button and the robot must execute a 180 degree pivot and accelerate to 10 mph in the opposite direction. These turns can continue for several minutes so drifting of the heading is undesirable. The robot must also track the heading. The rotation will be in about 360degrees per second. I am looking at a couple of possibilities:

Any suggestions would be greatly appreciated!