A remotely operated vehicle stabilizing problem, known as ROV-Observer for sub-sea historical sites observation, is addressed in this paper. To success this task, a first part of our study consists to reduce the complexity of the total dynamic model, hence, a rigorous formulation for the control objectives. A constant surge velocity as part of the equilibrium is considered, and around this vector of state a kino-dynamic model is addressed. As only positions are available, the stabilizing control objectives integrate an observation model to the ROV's local and global velocities. We prove that the ROV is asymptotically stable at the equilibrium. The effectiveness of these results are shown in simulation.