An Optimized Calculation Algorithm of Incidence Angle Based on Adaptive Newton Descent Method

Accurate determination of incidence angles in acoustic ray tracing is essential for enhancing the precision of global navigation satellite system-acoustic (GNSS-A) underwater positioning. However, the conventional iteration method often suffers from divergence or instability when dealing with large incidence angles, thus limiting its applicability in high-precision underwater positioning. To address this limitation, this study proposes an improved Newton iteration method based on weighting strategies derived from stochastic models. An adaptive descent factor is introduced to dynamically adjust weight values according to the magnitude of the incidence angle. Experimental validation using both real and simulated datasets demonstrates that the proposed adaptive Newton descent method significantly enhances accuracy and stability in solving for large incidence angles. Notably, when the cosine function is employed as the weighting function, the proposed method maintains stability even at large incidence angles (>81°), where the traditional iteration method fails or becomes unstable. Results indicate that the unit weight error is reduced to 0.4014215 m, with an average of six iterations per solution. This approach provides a novel and effective solution for calculating incidence angles in high-precision underwater positioning and holds considerable promise for applications in seafloor geodetic network construction and underwater engineering.