I would just walk the GPS positions, and compute the closest angular distance to the expected track.

Note that unless the vehicle is very slow, or the GPS have a very high update speed (say 10 $GPRMC strings/second), then the distance between two coordinates can be way longer than the distance between the measured path and the expected path. That makes it important to not just look at the sampled points, but the line connecting the samples.

Another problem is that the error from the GPS will slowly jitter, which means that after some time, the GPS data may be off to the other side of the road. This can best be seen by sampling the positions from a parked vehicle during a couple of hours.

The problem isn't so much to decide if you are following the path. It just a sqrt(dxi^2 + dxj^2 + ...) equation showing that the square of the distance between measured point and track is low for a couple of consecutive points.

The big problem is if you are going to use the computations to steer the vehicle, since the error signals because of GPS inaccuracies are so high. It some part, you can improve your situation by adding gyros/accelerometers and integrate between the measured positions/directions/speeds and the turn/acceleration speeds measured. Without looking at rotations/accelerations, it is very, very easy to create an unstable system that constantly oversteers and corrects.