A Novel Cooperative Localization Algorithm Based on LSTM and Factor Graph for AUV Swarms

To address localization error accumulation in autonomous underwater vehicle (AUV) swarms due to underwater acoustic communication interruptions, this paper proposes a cooperative localization method that integrates Long Short-Term Memory (LSTM) prediction and factor graph optimization. During the real-time stage, each AUV uses a trained LSTM to predict observations, ensuring the Unscented Kalman filter (UKF) maintains continuous state estimation during interruptions and mitigates error accumulation. During the post-processing stage, a factor graph comprising motion model factors, cooperative observation factors, and LSTM prediction factors is constructed on the AUV swarm master node. By adaptively switching factor types based on communication status, global nonlinear optimization is performed on the AUV states. Simulation results show that compared with UKF + LSTM, the proposed method reduces the Average Localization Error (ALE) by 55% and the Root Mean Square Error (RMSE) by 60%; compared with the Rauch–Tung–Striebel (RTS) smoothing algorithm, it reduces the ALE by 36% and the RMSE by 44%. This fully verifies that the strategy combining real-time state maintenance and post-processing global optimization can more effectively correct AUV localization errors in communication-interrupted regions. Experiments under different communication interruption durations further confirm the robustness of the proposed algorithm, with the maximum error-to-range ratio remaining below 0.2% of the range.