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The development of effective target tracking and collision avoidance algorithms is essential to the success of unmanned aerial vehicle (UAV) missions. In a dynamic environment, path planning for UAVs is often based on predicted obstacle and target motion. In this paper, an extended Kalman filter (EKF) is first used to estimate the states of a moving object detected by a UAV from its measured position in space. The optimal object trajectory is then predicted from the estimated object states and using the motion model defined for Kalman filtering. Finally, the quality of the predicted trajectory is evaluated by computing the variance of the prediction error. Simulation results are presented to demonstrate the effectiveness of the proposed approach.