Distance-Decay Effect in Probabilistic Time Geography for Random Encounter

Probabilistic time geography uses a fixed distance threshold for the definition of the encounter events of moving objects. However, because of the distance-decay effect, different distances within the fixed threshold ensure that the encounter events do not always have the same possibility, and, therefore, the quantitative probabilistic time geography analysis needs to consider the actual distance-decay coefficient (DDC). Thus, this paper introduces the DDC and proposes a new encounter probability measure model that takes into account the distance-decay effect. Given two positions of a pair of moving objects, the traditional encounter probability model is that if the distance between the two positions does not exceed a given threshold, the encounter event may occur, and its probability is equal to the product of the probabilities of the two moving objects in their respective positions. Furthermore, the probability of the encounter at two given positions is multiplied by the DDC in the proposed model, in order to express the influence of the distance-decay effect on the encounter probability. Finally, the validity of the proposed model is verified by an experiment, which uses the tracking data of wild zebras to calculate the encounter probability, and compares it with the former method.