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This study investigates the tracking of underwater cables using autonomous underwater vehicles (AUVs) equipped with side-scan sonar (SSS). AUV motion stability is crucial for effective SSS imaging, which is essential for continuous cable tracking. Traditional methods that derive AUV guidance rates directly from measured cable states often cause unnecessary jitter when imaging, complicating accurate detection. To address this, we propose a non-myopic receding-horizon optimization (RHO) strategy designed to maximize cable imaging quality while considering AUV maneuvering constraints. This strategy identifies the optimal heading decision sequence over a future horizon, ensuring stable and efficient cable tracking. We also employ a long short-term memory (LSTM) network to predict future cable states, further minimizing AUV motion instability during abrupt path changes. Given the computational limitations of AUVs, we have developed an efficient decision-making framework that can execute resource-intensive algorithms in real time. Finally, the robustness and effectiveness of the proposed algorithm were validated through comparative experiments. The results demonstrate that the proposed method outperforms existing methods in key metrics such as cable-tracking accuracy and AUV motion stability. This ensures that the AUV can acquire high-quality acoustic images of the submarine cable in an optimal state, enhancing the continuity and reliability of cable-tracking tasks. [ABSTRACT FROM AUTHOR]