GRKAN: Gate Recurrent Kolmogorov–Arnold Networks for UUV Noncooperative Target Trajectory Tracking

Noncooperative underwater target trajectory tracking is essential for enabling uncrewed underwater vehicles (UUV) to perform precise guidance, collision avoidance, and target capture tasks. Traditional Bayesian methods, which rely on predefined predictive and measurement models, have demonstrated limited effectiveness due to inherent uncertainty in underwater sonar observations and the unpredictable dynamics of noncooperative targets. To address these challenges, this article proposes a novel approach to developing gate recurrent Kolmogorov–Arnold networks (GRKAN) for UUV noncooperative target trajectory tracking. Unlike conventional methods that require explicit target dynamics and sonar observation parameters to construct predictive models, GRKAN reformulates tracking as sequence-based learning. This approach learns patterns of target motion and sonar observations from historical data to build a predictive model for noncooperative target trajectories. The GRKAN incorporates two key innovations: first, a recurrent Kolmogorov–Arnold representation for maintaining short-term memory of system states, and second, gating mechanisms for efficient information flow management. Furthermore, by integrating the Monte Carlo principle with GRKAN, we develop a sampling strategy within the observation space to address the uncertainty of posterior distributions. Experimental results demonstrate that the GRKAN-based approach significantly improves the accuracy and stability of noncooperative target trajectory tracking, particularly under conditions of uncertain observation.