Gait is a behavioral biometric trait that enables non-invasive person recognition based on individual walking patterns. Camera-based gait acquisition is convenient, but silhouette sequences often contain substantial motion-irrelevant appearance information, such as body shape, clothing, and carried objects. To address this problem, a multi-scale time series differencer is proposed to acquire tensor difference data between adjacent frames, so as to extract dynamic feature information in motion gait image sequences. Experiments on the CASIA-B dataset show that the proposed method achieves Rank-1 accuracies of 97.7%, 94.6%, and 80.0% under NM, BG, and CL conditions, respectively. Ablation results further demonstrate that MTDU improves the mean accuracy from 84.7% to 90.8% compared with single-scale temporal differencing. The multi-scale time series differencer shows potential for fields including sports motion gait detection and recognition, surveillance security motion gait identity authentication, and medical motion gait recovery assessment for sports injuries, demonstrating practical application value.