Abstract-Maritime Situational Awareness is crucial in maritime operations to identify threats and to deal with them as soon as possible. These threats can be pirates in shipping operations, icebergs when sailing in the northern sea routes, or even unknown vessels or objects that might be on the ship's path. A solution to identify these threats is the use of UAV's to overfly the ship's planned path. This solution is described in this paper, using an autonomous fixed wing UAV. Based on the provided ship's planned path, the UAV should autonomously map the area close to the ship track. To do that, an optimization problem is solved using Model Predictive Control, where the turn rate for the next time period is optimized. Based on the turn rate, the future path of the UAV is calculated and the waypoints are sent to the autopilot. This application is thoroughly tested using a Software In Loop environment, where an aircraft model is used with the autopilot's simulation. The results show that surveillance performance is improved if the UAV has information about the ship's velocity in addition to position.