Three-Dimensional CKANs: UUV Noncooperative Target State Estimation Approach Based on 3D Convolutional Kolmogorov-Arnold Networks

Accurate and stable estimation of the position and trajectory of noncooperative targets is crucial for the safe navigation and operation of sonar-equipped underwater unmanned vehicles (UUVs). However, the uncertainty associated with sonar observations and the unpredictability of noncooperative target movements often undermine the stability of traditional Bayesian methods. This paper presents an innovative approach for noncooperative target state estimation utilizing 3D Convolutional Kolmogorov-Arnold Networks (3DCKANs). By establishing a non-Markovian model that characterizes state estimation of UUV noncooperative targets under uncertain observations, we leverage historical data to construct 3D Convolutional Kolmogorov-Arnold Networks. This network learns the patterns of sonar observations and target state transitions from a substantial offline dataset, allowing it to approximate the posterior probability distribution derived from past observations effectively. Additionally, a sliding window technique is integrated into the convolutional neural network to enhance the estimator's fault tolerance with respect to observation data in both temporal and spatial dimensions, particularly when posterior probabilities are unknown. The incorporation of the Kolmogorov-Arnold representation within the convolutional layers enhances the network's capacity for nonlinear expression and adaptability in processing spatial information. Finally, we present statistical experiments and simulation cases to validate the accuracy and stability of the proposed method.