Underwater vehicles are rich systems with attractive and challenging properties such as nonlinearities, external disturbances, and underactuated dynamics. These make the design of an advanced and robust controller quite a challenging task. This paper focuses on designing a model-free high-order sliding mode controller in a six-degree-of-freedom trajectory tracking task. The purpose of the control is accurate trajectory tracking and considerably reducing the chattering phenomenon in situations where the remotely operated vehicle (ROV) works in the presence of external disturbances, measurement errors, and actuator dynamics and nonlinearity, which is not seen in previous research. To demonstrate the stability of the closed-loop system, the Lyapunov theory is employed to ensure the asymptotic stability of tracking errors. A linear Kalman filter for estimating measurement errors is proposed to be used to correct positioning system outputs (speed, position, and attitude). In a hardware-in-the-loop test, the proposed controller for the ROV is tested in a real-time application, considering external disturbances, measurement errors, and actual thrusters. In addition, comparing the outcomes with the performance of the PID controller and the supper twisting controller shows the superiority of the proposed controller. Due to the existence of the measurement noise, spectrum analysis is also performed.