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Time geography considers that the probability of moving objects distributed in an accessible transportation network is not always uniform, and therefore the probability density function applied to quantitative time geography analysis needs to consider the actual network constraints. Existing methods construct a kernel density function under network constraints based on the principle of least effort and consider that each point of the shortest path between anchor points has the same density value. This, however, ignores the attenuation effect with the distance to the anchor point according to the first law of geography. For this reason, this article studies the kernel function framework based on the unity of the principle of least effort and the first law of geography, and it establishes a mechanism for fusing the extended traditional model with the attenuation model with the distance to the anchor point, thereby forming a kernel density function of time geography under network constraints that can approximate the theoretical prototype of the Brownian bridge and providing a theoretical basis for reducing the uncertainty of the density estimation of the transportation network space. Finally, the empirical comparison with taxi trajectory data shows that the proposed model is effective.

Modeling of Time Geographical Kernel Density Function under Network Constraints