Space-Time Prism Model

DEFINITION During the last decade, the proliferation of location-aware devices, such as GPS and smartphones, has given rise to the collection of huge amounts of moving object data in the form of finite sequences of time-stamped geographical locations. These sequences of space-time points encode (a sample of) the trajectories of moving objects. The location of the moving objects is unknown between these measured space-time points. Several models have been proposed to model the uncertainty of a moving object’s location in between sample points. Linear interpolation between the sample points is a first and obvious example. However, if additional information is available, such as a limit on the possible speed of a moving object, a more informative model is provided by the framework of space-time prisms. This model gives, between two consecutive measured locations, the envelope of possible locations of a moving object in space-time space, given an upper bound on the moving object’s speed. In the context of space-time prisms, the measured space-time points are usually called anchor points. A space-time prism between two anchor points is a geometric object in space-time space that enclosed all locations where the moving object can possibly have been, given the measured locations, the time interval between them and the object’s speed bound. The projection of a space-time prism on the spatial component of space-time space is an ellipse which delimits the collection of possible locations that the moving object can have visited. The collection of space-time prisms between a sequence of anchor points is referred to as a chain of space-time prisms. Here, it should be clear that the upper bound on the object’s speed may differ from location to location and can be regarded as geographical background information. Figure 1 depicts an example of a space-time prism between two consecutive anchor points and a chain of space-time prisms between a sequence of anchor points with varying local speed bounds.