In recent years, robots have attracted attention to provide a supplemental workforce in Japan as the working population decreases. A reception and response control system using the interface robot ApriPoco™ has been studied, measuring human walking trajectories using a laser range finder, but accurate measurements have been impeded by overlapping people and trajectories leading to missing data. Therefore, in this paper, we propose a system that uses Gaussian process regression to predict human trajectories in addition to the conventional system. Three-directional walking experiments were conducted with groups of one, three, and five people, and the trajectories of the conventional and proposed systems were compared. The experimental results show that the proposed system has fewer missing data than the conventional system and can obtain more accurate trajectories. We also demonstrated human walking-trajectory measurement at a public museum to confirm the effectiveness of this system. In the future, we plan to build a reception system by linking this system with robots.