7. Two Dimensional Jerk Modeling: Jump-Diffusion Approach

Building upon conventional microscopic traffic flow models, the preceding chapters introduce lateral treatment to enhance their effectiveness. These models are formulated based on specific assumptions. To validate their accuracy, a comparison is made between theoretical and realistic trajectories. However, the significance of another crucial factor, jerk, in influencing traffic safety cannot be overlooked. It is imperative for these models to accurately reproduce jerk profiles consistent with real-world observations, particularly in the context of autonomous vehicle testing. In this chapter, we demonstrate that existing microscopic traffic flow models fail to generate realistic jerk profiles through a theoretical derivation of jerk distribution and simulation. To address this limitation, we propose an innovative jump-diffusion approach that captures the stochastic nature and jerk component. By incorporating a jump term characterized by the Poisson distribution into the original diffusion-type microscopic traffic flow model, we construct a numerical scheme for the jump-diffusion equation. Our results indicate that the proposed approach successfully captures jerk profiles observed in real-world datasets. The adoption of this approach significantly enhances the realism and applicability of microscopic traffic flow models in autonomous vehicle testing scenarios. It provides a valuable contribution to the field by addressing the challenge of accurately representing jerk profiles, thereby improving the safety assessment of autonomous vehicles.