There has been extensive study of the target tracking problems in the recent years. Very little work has been done in the problem of continuous monitoring of all the mobile targets using the fewest number of mobile trackers, when the trajectories of all the targets are known in advance. Almost all the existing research discretized time (and/or space), or assume infinite tracker velocity. In this thesis, I consider the problem of covering (tracking) target nodes using a network of Unmanned Airborne Vehicles (UAV's) for the entire period of observation by adding the constraint of fixed velocity on the trackers and observing the targets in continuous time and space. I also show that the problem is NP-complete and provide algorithms for handling cases when targets are static and dynamic.