## 1 Introduction
[PERSON] and [PERSON] derived an adaptive control law for a six-degree-of-freedom (6-DOF) model for the trajectory tracking problem of an underactuated underwater vehicle in the presence of a parametric uncertainty [15]. [PERSON] et al. proposed to control ROVs for exploration in sub-sea historical sites and designed a nonlinear observer to estimate the linear and angular velocity of an ROV [16]. [PERSON] et al. developed a new adaptive neural network control approach for a class of ROVs and introduced an adaptive observer for the velocity state and angular velocity state estimation with a local recurrent neural network [17]. In complex missions, an ROV often requires a high degree of autonomy, precision, and maneuverability. Moreover, a single sensor is not sufficient to obtain the position and velocity information of the ROV because each type of sensor has its own disadvantages. Thus, ROVs are usually equipped with different types of sensors, such as the inertial measurement unit (IMU) and the velocity log [18]. The IMU can measure the linear accelerations and the rotational velocity of the vehicle. Further, the velocity log, usually a Doppler velocity log (DVL), can measure the linear velocities of the vehicle. The IMU and the DVL measurements are usually combined to provide stable linear velocity, angular velocity, and orientation signals. Depending on the quality of the onboard IMU, the position of the vehicle can be computed from the linear acceleration and velocity measurements. However, because of the inevitable drift in the IMU and DVL, the position estimate will not be stable over time. When the ROV swims through the water, ocean currents always have an influence on the motion of the ROV. To increase the performance, accuracy, and the situation awareness of the ROV, the estimation of the ocean current velocity is often desired. However, the IMU can only measure the total acceleration experienced by the vehicle and cannot distinguish between the motion induced by the ocean current and that induced by the onboard propulsion system. Moreover, the DVL cannot measure the ocean current velocity in its usual configuration. As the hydrodynamic forces acting on the ROV depend on the velocity of the vehicle with respect to the water, but not the total velocity of the vehicle with respect to the fixed coordinate frame, obtaining the ocean current velocity information can considerably improve the performance of the vehicle control system. For ocean currents, researchers have developed a variety of observers to estimate the current velocity. [PERSON] et al. designed an exponentially stable current observer for a reduced-order dynamic vehicle model, and used the estimated current velocity to compute the hydrodynamic forces and moments more accurately for inclusion in a feedback control strategy. Further, the observer only required position measurements [19]. [PERSON] and [PERSON] proposed an estimation scheme and designed a kinematic observer for ocean current estimation. The proposed observer provides exponential convergence to the true ocean current velocity, but requires the knowledge of both the position and the relative velocity of the vehicle [20]. [PERSON] et al. took a model-based approach and designed a six-degree-of-freedom (6-DOF) observer for the ocean current velocity on the basis of the dynamic model and the measurement of the linear velocity of the vehicle [21]. The deep sea ROV systems typically consist of a large support vessel, a winch, umbilical cable, and ROV. Thus far, most of the research has focused on the numerical simulation and prediction of the cable configuration and the ROV motion with the cable effect [22; 23; 24]. However, few studies have dealt with motion control models for ROVs considering the cable disturbing force and the current effects because of the corresponding complexity and difficulty. As the ocean current velocity and the cable disturbing force cannot be measured by the standard onboard sensors, the development of an estimation scheme is required.