Movement of objects is taking place in geographical contexts. Context directly/indirectly influences movement process and causes different reactions to moving objects. Therefore, considering context in movement studies and the development of movement models are of vital importance. In this regard, incorporating context can play a crucial role in similarity measurement of objects movements and their corresponding trajectories. Trajectories of moving point objects, beside their spatial and temporal dimensions, have another aspect which is called contextual dimension. This dimension, however, has been less considered so far and a few researches in trajectory analysis domain have investigated it. To this end, this research develops a method based on Euclidean distance in which individual spatial, temporal, and contextual dimensions as well as their integration can be explored in the process of similarity measurement of trajectory. Beside the simplicity of the method, it is developed in a way for taking into account every small change in each type of dimension(s). To validate the proposed method and survey the role of contextual data in similarity measurement of trajectories, three experiments are performed on commercial airplane dataset. Accordingly, geographical coordinates and altitude of airplane as spatial dimension, travel time as temporal dimension, and airplane speed, wind speed, and wind direction as contextual dimension are utilized in these experiments.

The first experiment measures the correspondence of trajectories in different dimensions. Also, it explores the role of dimensions weights individually and collaboratively along the similarity measure process. The results demonstrate that weights severely affect similarity values, while they are totally application dependent. Meanwhile, it can be confirmed that contexts may increase or decrease the values of trajectories similarities. This effect can be seen in the average of relative similarity values of commercial airplanes trajectories in spatial (0.60), spatial-temporal (0.51), and spatial-temporal-contextual (0.46) dimensions. Contexts can enhance and restrict movements as well. To justify this statement, the second experiment is conducted to explore how movement and geographical contexts interact in similarity measure process. To this end, four sample trajectories are compared with respect to different dimensions. For a pair of trajectory, the relative similarity value at spatial dimension is 0.04. By incorporating time dimension, this value increases to 0.30 at spatio-temporal dimension. Given the high similarity of these two trajectories in wind direction, wind speed, and airplane speed (0.85), the ultimate similarity of them becomes 0.48. In contrast, for another pair of trajectory, the spatial and spatio-temporal similarity values are 0.85 and 0.91, respectively. Considering the similarity value of these two trajectories in wind direction, wind speed, and airplane speed (0.37), the final relative similarity becomes 0.73. The third experiment sought for the role of motivation context in similarity measure process. Although such context is very difficult to capture and in many applications will remain inaccessible, we consider the pilots decisions in handling the airplanes during the approaching and landing phases (i.e., continuous descent final approach or dive and drive) as the motivation context in this application. Choosing either of these techniques highly affects the figure of trajectories where quantifying them can be accomplished by measuring the similarity of trajectories at spatial and spatial-temporal dimensions. All in all, the results of the above experiments yield the robustness of the proposed method in similarity measurement of trajectories as well as its sensitivity to slight alterations in dimensions.