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.

翻译：我们考虑了在基于车辆轨迹拟合基本图时，速度-密度数据中非局部性的作用。我们证明，使用预期密度能够将速度-密度数据清晰分类为稳态点与非稳态点，即加速与减速区域及其分隔边界。该分隔边界代表稳态交通状态的轨迹，即基本图。为了拟合基本图，我们开发了一种增强的交叉熵最小化方法，该方法遵循平衡交通物理特性。通过将我们的方法与使用局部速度-密度状态和最小二乘估计的传统方法进行比较，我们展示了所提出方法的有效性。实验表明，在相同时空区域内，我们的方法中的分隔边界对不同轨迹样本保持不变，这进一步证明了分隔边界确实是稳态交通状态的轨迹。