## 1 Introduction
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Category** & **Reference** & **Method** & **Description and Conclusions** \\ \hline LSTM variants & [35; 36; 37; 38] & Multiscale attention-based LSTM, self-attention LSTM (SALSTM), LSTM, LSTM with multi-head attention & Various LSTM variants have been proposed, including multiscale attention, self-attention, and multi-head attention LSTMs, to improve prediction accuracy for ship motion, roll, surge, and pitch by enhancing robustness and handling different input-output ratios. \\ \hline Deep learning and attention mechanism models & [24; 25; 39] & Hybrid RNN, LSTM, Transformer, weighted attention model & Transformers, and weighted attention models, have been used for real-time predictions of ocean currents and AUV navigation, enhancing prediction accuracy across broad temporal and spatial ranges. \\ \hline Data decomposition and hybrid models & [26; 40] & VMD-BiGRU, TVF-EMD + SVR & Data decomposition and hybrid models like VMD-BiGRU and TVF-EMD + SVR developed to improve the accuracy of short-term buoy motion and ship roll predictions by addressing frequency-specific patterns, nonlinearity, and time-varying dynamics. \\ \hline \hline Informer and Its Variants & [27; 41] & Conv-Informer, SSA-Optimized CEEMDAN-Informer & Informer variants, such as Conv-Informer and SSA-Optimized CEEMDAN-Informer for multi-step and long-sequence ship motion predictions, capturing both local and long-range dependencies, and enhancing performance across varied sea conditions. \\ \hline Multi-model and combination methods & [10; 28] & Multi-model machine learning, combination model & Multi-model and combination methods like confidence-based machine learning and optimized weighting models improve the prediction accuracy of ship stability and surfacing positioning for underwater gliders across different time scales. \\ \hline \hline \end{tabular}
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Table 1: Studies related to underwater glider parameter prediction. glider data, thereby improving the prediction of dynamic behaviors over time [49]. These models can learn from sequential data and provide robust predictions, even in the presence of noise and missing data, which are common in marine environments [50; 51]. This paper proposes a novel method termed DFFormer to predict UG control parameters, with a particular focus on rudder angles. The proposed method integrates discrete wavelet transform (DWT) for rudder angle signal decomposition of the rudder angle and employs a fast Fourier transform-based attention mechanism (FFT-Attention) to effectively capture and analyze its frequency- and time-domain characteristics. Notably, the method leverages a Transformer architecture to process the decomposed signals through multiple parallel pathways, substantially improving the capability to forecast the complex and variable UG control parameters. The incorporation of an attention mechanism significantly bolsters the model's capacity to identify pivotal features within time-series data, culminating in a more robust and dependable forecasting framework. The efficacy of the proposed method is validated through actual sea trials. The results demonstrate significant improvements in UG prediction accuracy and operational efficiency of UGs, thereby enhancing their heading-keeping ability. This study not only advances the field of underwater vehicle parameter prediction but also offers valuable insights for the application of deep learning techniques in other types of autonomous underwater systems. The rest of this paper is organized as follows: Section 2 introduces the modeling approach for underwater gliders and the working principles of the proposed DFFormer method, focusing on the kinematic equations, control strategies, and the design and implementation of the discrete wavelet transform, fast Fourier transform-based attention mechanism, and recursive layers. Section 3 presents the experimental results and analysis, comparing the performance of various prediction methods using actual sea trial data.