If the umbilical of Remote Operated Vehicle (ROV) allows the transmission of information in real time or the supply of energy to the robot, it also has many disadvantages such as entanglement or the difficulty of predicting its shape, which raises the question of being able to do without it. In order to turn these constraints into advantages, this paper proposes a method to estimate the position of an ROV by observing the shape of its umbilical. The umbilical is equipped with moving ballasts and buoys to give it a predictable shape with straight lines: simple mathematical models of the umbilical can thus be defined. Using these models and measuring the angles at the ends of the cable, the position of the ROV can be found. Three umbilical models with different equipment are proposed. The methods were tested in a pool and the estimated position of the ROV was compared with its actual position measured using a motion capture system.