<p>Accurate modeling of higher-order harmonics is crucial for optimizing the performance of underwater acoustic parametric arrays, yet traditional adaptive identification methods often fail to effectively capture these components under low-order kernel functions. To address this challenge, we propose an innovative adaptive filtering framework based on Function-Link Artificial Neural Networks (FLANN) employing trigonometric expansion, supported by square-root amplitude modulation. Specifically, we introduce two novel models: the Audio-to-Audio Trigonometric Filter (A2TF) and the Ultrasound-to-Ultrasound Trigonometric Filter (U2TF). Theoretical and simulation analysis, along with tank and lake experiments demonstrate that the A2TF model achieves comparable modeling accuracy for lower-order harmonics as the traditional A2 One-Dimensional Volterra Filter (A2ODVF), while significantly enhancing the fitting capability for higher-order harmonics. Furthermore, the U2TF model exhibits superior performance in scenarios characterized by severe original wave distortion, yielding notably lower steady-state errors compared to the U2 One-Dimensional Volterra Filter (U2ODVF). This research advances the field by providing a robust and efficient technical solution for adaptive modeling of propagation paths in underwater acoustic parametric arrays, offering both theoretical insights and practical applicability.</p>