A Detailed View on the Spatio-Temporal Information Content and the Arithmetic Coding of Discrete Trajectories

The trace of a moving object is commonly referred to as a trajectory. This paper considers the spatio-temporal information content of a discrete trajectory in relation to a movement prediction model for the object under consideration. The information content is the minimal amount of information necessary to reconstruct the trajectory, given the movement model. We show how the information content of arbitrary trajectories can be determined and use these findings to derive an approximative arithmetic coding scheme for trajectory information, reaching a level of compression that is close to the bound provided by its entropy. We then demonstrate the practical applicability of our ideas by using them to compress real-world vehicular trajectories, showing that this vastly improves upon the results provided by the best state-of-the art compression schemes for spatio-temporal data.