Which of the following degrees of freedom can be controlled by a Dynamic Positioning system and is not influenced by a position reference system?

The degree of freedom that can be effectively controlled by a Dynamic Positioning (DP) system without the influence of a position reference system is yaw. Yaw refers to the rotation around the vertical axis, which allows a vessel to change its heading or orientation.

In a DP system, yaw control is managed primarily through the use of thrusters and rudders, which adjust the vessel's heading automatically based on predetermined set points or commands from the DP control system. This control does not require position reference inputs because it is based on the vessel's ability to steer and maneuver without needing to know its precise location in relation to a fixed point.

Other degrees of freedom like surge (forward and backward movement), sway (sideways movement), and heave (vertical movement) typically rely on position reference systems to maintain a vessel’s position and prevent drift due to environmental forces. The successful management of these movements involves constant feedback from sensors that track the vessel's position relative to other points, making them dependent on a position reference system. Thus, the ability to control yaw independently of position references distinguishes it as the correct answer in this context.