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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.

Based on probabilistic time-geography, the encounter between two moving objects is random. The quantitative analysis of the probability of encounter needs to consider the actual geographical environment. The existing encounter probability algorithm is based on homogeneous space, ignoring the wide range of obstacles and their impact on encounter events. Based on this, this paper introduces obstacle factors, proposes encounter events that are constrained by obstacles, and constructs a model of the probability of encounters of moving objects based on the influence of obstacles on visual perception with the line-of-sight view analysis principle. In realistic obstacle space, this method provides a quantitative basis for predicting the encountering possibility of two mobile objects and the largest possible encounter location. Finally, the validity of the model is verified by experimental results. The model uses part of the Wuhan digital elevation model (DEM) data to calculate the encounter probability of two moving objects on it, and analyzes the temporal and spatial distribution characteristics of these probabilities.