In this paper, we introduce a set of novel distance metrics that use model based representations for trajectories. We determine the similarity of trajectories using the conformity of the corresponding HMM models. These metrics enable the comparison of tracjectories without any limitations of the conventional measures. They accurately identify the coordinate, orientation, and speed affinity. The proposed HMM based distance metrics can be used not only for ground truth comparisons but for clustering as well. Our experiments prove that they have superior discriminative properties.