We consider the role of non-localities in speed-density data used to fit fundamental diagrams from vehicle trajectories. We demonstrate that the use of anticipated densities results in a clear classification of speed-density data into stationary and non-stationary points, namely, acceleration and deceleration regimes and their separating boundary. The separating boundary represents a locus of stationary traffic states, i.e., the fundamental diagram. To fit fundamental diagrams, we develop an enhanced cross entropy minimization method that honors equilibrium traffic physics. We illustrate the effectiveness of our proposed approach by comparing it with the traditional approach that uses local speed-density states and least squares estimation. Our experiments show that the separating boundary in our approach is invariant to varying trajectory samples within the same spatio-temporal region, providing further evidence that the separating boundary is indeed a locus of stationary traffic states.

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