Multi-person tracking is a very difficult problem in Computer Vision as a tracking algorithm is facing several issues, such as appearance changes, targets' occlusions and similar appearances between people. In an online tracking-by-detection algorithm, robust and discriminative specific appearance models help handling these difficulties. As done in single object tracking, we use sparse representations to extract local features of the targets and study how these representations can be specifically employed for multi-person tracking. Experiments on several datasets show that considering spatial information is crucial in order to improve the tracking performances with local descriptions compared to holistic features. Using large collaborative representations also improve the tracking results by naturally discarding irrelevant local patches.