KAN-Former: 4D Trajectory Prediction for UAVs Based on Cross-Dimensional Attention and KAN Decomposition

To address the core challenges of multivariate nonlinear coupling and long-term temporal dependency in 4D UAV trajectory prediction, this study proposes an innovative model named KAN-Former. On a 21-dimensional multimodal UAV dataset, KAN-Former achieves statistically significant improvements over all baseline models, reducing the mean squared error (MSE) by 8.96% compared to the standard Transformer and by 2.66% compared to the strongest physics-informed baseline (PITA), while decreasing the mean absolute error (MAE) by 7.43% relative to TimeMixer/PatchTST. The model adopts a collaborative architecture with two key components: first, a “vertical–horizontal” cross-dimensional attention mechanism—where the vertical branch models physical correlations among multivariate variables using hierarchical clustering priors, and the horizontal branch employs a blockwise dimensionality reduction strategy to efficiently capture long-term temporal dynamics; second, it represents the first application of Kolmogorov–Arnold decomposition in trajectory prediction, replacing traditional feedforward networks with learnable combinations of B-spline basis functions to approximate high-dimensional nonlinear mappings. Ablation studies verify the effectiveness of each module, with the KAN module alone reducing MSE by 6.59%. Moreover, the model’s feature clustering results align closely with UAV physical characteristics, significantly improving interpretability. The demonstrated improvements in accuracy, interpretability, and computational efficiency make KAN-Former highly suitable for real-world applications such as real-time flight control and air traffic management, providing reliable trajectory forecasts for decision-making systems. This work offers a new paradigm for trajectory prediction in complex dynamic systems, successfully integrating theoretical innovation with practical value.