This paper is concerned with the finite horizon H_∞ filtering problem of linear discrete-time, time-varying systems using a direct approach based on the completing-the-square. We derive a necessary and sufficient condition for the existence of the H_∞ filters, and give the parametrization of all linear H_∞ filters. In particular, the time-updating H_∞ filtering algorithm is explicitly shown. Furthermore, we investigate a possibility of the real-time application of the H_∞ filters to a robotic visual tracking system. The simulation results show that the derived H_∞ filtering algorithm is quite effective for the robotic visual tracking applications.