## 1 Introduction  
Unmanned surface vessel (USV) as an intelligent and autonomous marine equipment has received more and more attention from the control community, for broad application in the cluttered ocean environment, especially in cases where human intervention is not possible [1]. Generally speaking, three different types of control technologies play a crucial role in the development of USVs: path following control, trajectory tracking control and set-point control [2]. Many researchers propose lots of relevant control strategies and address the issues to a various extent. This study continues along the works and contributions of the predecessors. This paper aims at the path following control, mainly discussing the guidance and control of a USV. Path following is usually defined as steering a vessel to follow the desired path at a certain speed, which is not specified with temporal constraint [3]. Although there are considerable theoretical studies regarding the path following and practical engineering achievements, practical studies of the path following control for USVs have progressed haltingly amid great difficulties. It is essential to develop a highly accurate and robust path following controller for a USV when executing various vital missions. Therefore, under the circumstance of severe sea state, the safe operation and mission execution can be guaranteed. Two aspects play crucial roles in the path following control scheme: guidance and control [4]. Guidance can refer to the popular and effective line-of-sight (LOS) guidance, refining missile guidance approach or marine guidance [5; 6]. This special guidance law exploits the geometry relationships to generate a yaw angle known as the approaching angle, which is fed into the control system. In other words, the control system tracks the reference yaw angle signal together with the specified velocity tracking. Hence, the performance of the path following heavily depends on the guidance system. It turns out that classic LOS guidance is simple and effective [7], albeit with limitations in the case of being exposed to the complex ocean environment induced by waves, wind, and ocean currents. Moreover, the traditional LOS guidance will cause large cross-tracking error when the marine surface vehicles are in steady state, which strictly depends on the path curvature and the magnitude of the drift force. Therefore, the traditional LOS was extended to various forms such as integral LOS (ILOS) guidance and adaptive LOS (ALOS) guidance by [PERSON]. In [8], an ILOS guidance with integral action is proposed to handle the constant and irrotational ocean currents and other environmental disturbances including wind or waves. In [9], a new ILOS with time-varying lookahead distance is presented with the capability of canceling the effects of constant environmental disturbances, like constant ocean currents. In [10], the direct and indirect adaptive ILOS based path following controller is proposed to deal with the ocean currents. Another way to improve the LOS guidance is to estimate the sideslip angle caused by the external disturbance as an observer-based strategy. In [11], a novel adaptive LOS (ALOS) guidance with small computation footprint is proposed where the adaptive laws dominate the sideslip angle compensation rate. The sideslip angle is treated as an unknown constant, which significantly limits the application of ALOS. In [12], a reduced-order extended state observer (ESO) based LOS guidance is proposed to deal with the time-varying sideslip angle, which is appropriate for straight-line and curved path following. In [13], the magnitude and convergence speed of the sideslip angle is considered, which can be identified by the constructed finite-time sideslip angle observer. However, on the one hand, it should be noted that the aforementioned literature (e.g., [8; 9; 10]) merely solve the problem in the kinematic level, i.e., ignoring the along-tracking error.