Cauchyian Motion: A Spatio-Temporal Scale Invariant Mobile Trajectory Model

Human mobility is a complex phenomenon driven by spatial interactions and temporal dynamics. The study of mobility patterns has far-reaching implications, from designing efficient transportation systems to responding effectively to epidemics. In this paper, a univariate mobility model is developed using circular statistics to abstract human motion. The validity of this model is confirmed through the analysis of a real-world GPS dataset. The wrapped Cauchy distribution, which best-fits the turning angles and detrended bearings, is utilized to extract the distinctive features of straight-oriented shortest-path-first route. The proposed modeling aims to capture the inherent cyclic nature of mobile trajectories. By adjusting the scale parameter, the model can characterize mobility patterns at different spatial and temporal resolutions, thus facilitating accurate analysis, simulation, and prediction of mobile trajectories.