The quadruped robots have superior adaptability to complex terrains, compared with tracked and wheeled robots. Therefore, leader-following can help quadruped robots accomplish long-distance transportation tasks. However, long-term following has to face the change of day and night as well as the presence of interference. To solve this problem, we present a day/night leader-following method for quadruped robots toward robustness and fault-tolerant person following in complex environments. In this approach, we construct an Adaptive Federated Filter algorithm framework, which fuses the visual leader-following method and the LiDAR detection algorithm based on reflective intensity. Moreover, the framework uses the Kalman filter and adaptively adjusts the information sharing factor according to the light condition. In particular, the framework uses fault detection and multisensors information to stably achieve day/night leader-following. The approach is experimentally verified on the quadruped robot SDU-150 (Shandong University, Shandong, China). Extensive experiments reveal that robots can identify leaders stably and effectively indoors and outdoors with illumination variations and unknown interference day and night.