We present a variational technique for finding low curvature smooth approximations to trajectories in the plane. The method is applied to short segments of a vehicle trajectory in a known ground plane. Estimates of the speed and steering angle are obtained for each segment and the motion during the segment is assigned to one of the four classes: ahead, left, right, stop. A hidden Markov model for the motion of the car is constructed and the Viterbi algorithm is used to find the sequence of internal states for which the observed behaviour of the vehicle has the highest probability.