## 1 Introduction
While this approach increased the accuracy of heading control, the introduction of two extended state observers made it sensitive to parameter changes, thereby increasing complexity. [PERSON] et al. [32] proposed an improved line-of-sight (LOS) guidance algorithm that can adjust adaptively based on the path following error. The global asymptotically stable path-following controller was designed based on the nonlinear backstepping method and the Lyapunov stability theory. [PERSON] et al. [33] focused on unmanned vessels and mapped the desired inertial velocity to the desired body velocity. Their method used a new definition of vertical drift, combining the drift angle with the desired heading angle in a heading control strategy extended to the vertical plane. This effectively increased the rate of convergence. However, because of the simultaneous following of LOS vectors in two coordinate systems and the consideration of velocity allocation strategies, significant computational resources and time were required. Heading control strategies for robots are an essential component of robot path following [34; 35]. At present, control strategies based on the LOS method have been extensively researched and applied. These methods effectively improve control accuracy and system robustness and are widely used in practice. However, they also face challenges in terms of complexity and computational load [36]. Therefore, future research should aim to find simpler yet effective control strategies that meet the practical requirements of path following while ensuring control accuracy and performance. Path planning and following is a critical research area in UAV applications. In such research, the construction of an accurate reference path is a crucial step, as it determines the trajectory and motion state of the UAV. Previous research focusing on LOS following has produced a number of methods for constructing reference paths. [PERSON] et al. and [PERSON] et al. [37; 38] investigated specific geometric paths such as straight lines and circles, while [PERSON] et al. and [PERSON] et al. [39; 40] constructed reference paths composed of smooth curves, all of which resulted in commendable effectiveness. However, in practical engineering applications, task-oriented requirements often require the UAV to navigate and follow irregular paths, thus imposing certain limitations on the aforementioned methods. To further enhance the practical applicability of the following methods, [PERSON] et al. and [PERSON] et al. [41; 42] have guided UAVs to follow a sequence of path segments connected by given waypoints. However, there is still room for improvement in both following accuracy and convergence speed. To meet the requirements of engineering applications, this paper adopts path segments connected by waypoints as the reference paths and conducts 3D path-following research using LOS. Using the improved LOS method, this paper's approach facilitates the adjustment of control signals based on the UAV's actual following errors and the dynamic evolution of the reference path. This enables the UAV to follow the reference path more accurately. By using the improved LOS method, the approach proposed in this paper can adjust control signals based on the actual UAV following errors and changes in the reference path. This enables the UAV to follow the reference path with more accuracy. This paper proposes a strategy to improve the path-following accuracy of the FPLIR. This strategy is based on an improved LOS approach that takes into account the constraints of the robot's performance and the reference path information. Adaptive techniques are used to adjust the acceptance circle and heading control strategies. A path-following error equation is established, and a state-feedback-based control law is developed to achieve 3D path following, reduce following errors, and improve convergence speed. Numerical simulation experiments validate the effectiveness of the proposed method. The main contributions of the study are as follows:  
1.