CosIn: A statistical-based algorithm for computation of space-speed time delay in pedestrian motion

Precise assessment of Space-speed time delay (TD) is critical for distinguishing between anticipation and reaction behaviors within pedestrian motion. Besides, the TD scale is instrumental in the evaluation of potential collision tendency of the crowd, thereby providing essential quantitative metrics for assessing risk. In this consideration, this paper introduced the CosIn algorithm for evaluating TD during pedestrian motion, which includes both the CosIn-1 and CosIn-2 algorithms. CosIn-1 algorithm analytically calculates TD, replacing the numerical method of discrete cross-correlation, whereas the CosIn-2 algorithm estimates the TD from a statistical perspective. Specifically, the CosIn-1 algorithm addresses the precise computation of TD for individual pedestrians, while the CosIn-2 algorithm is employed for assessing TD at the crowd scale, concurrently addressing the imperative of real-time evaluation. Efficacy analyses of the CosIn-1 and CosIn-2 algorithms are conducted with data from single-file pedestrian experiments and crowd-crossing experiments, respectively. During this process, the discrete cross-correlation method was employed as a baseline to evaluate the performance of both algorithms, which demonstrated notable accuracy. This algorithm facilitate the precise evaluation of behavior patterns and collision tendency within crowds, thereby enabling us to understand the crowds dynamics from a new perspective.