摘要： 航海领域现有的轨迹相似性度量方法多以传统算法为主，计算复杂度较高，尽管已经提出了一些基于深度学习的方法,但存在空间-时间联合建模不足的问题，导致相似性度量的准确性和鲁棒性有待提升。针对上述问题，本文提出了MDU-net（Marine Density U-Net）模型，该模型能够自动提取船舶轨迹的低维特征，从而高效可靠地检索与指定目标相似的轨迹。首先对轨迹数据进行等时间间隔插值，再采用核密度估计生成融合空间与速度信息的核密度灰度图，实现轨迹像素化。随后，采用基于U-net结构的神经网络进行无监督学习，获得轨迹的低维表示；最终通过计算低维特征向量间的余弦距离构建相似矩阵，量化轨迹间的相似性。实验结果表明，MDU-net 在多个评估指标上显著优于传统方法与主流深度学习模型。与经典动态时间规整（DTW）方法相比，MDU-net前十条轨迹命中率提升了7.7个百分点；与Hausdorff相比提升约 14.7 个百分点。与深度模型对比，MDU-net 的优势更为突出，相较于卷积自编码器（CAE），前十条轨迹的命中率提升了25个百分点，充分验证了MDU-net在船舶轨迹相似性度量任务中的优越效果。

Abstract: Most existing trajectory similarity measurement methods in the maritime domain rely on traditional algorithms, which often suffer from high computational complexity. Although a few deep learning-based approaches have been proposed, some of them lack joint modeling of spatial and temporal features, resulting in limited accuracy and robustness in similarity measurement. To address these issues, this paper proposes a novel model named MDU-net (Marine Density U-Net), which can automatically extract low-dimensional features from ship trajectories, enabling efficient and reliable retrieval of trajectories similar to a specified target. Specifically, The trajectory data is first interpolated at equal time intervals, and then kernel density estimation is applied to generate grayscale maps that integrate spatial and velocity information, thereby achieving trajectory pixelization. Then, an unsupervised U-net-based neural network is employed to learn the low-dimensional representations of trajectories. Finally, cosine distance is calculated between the feature vectors to construct a similarity matrix and quantify trajectory similarities. Experimental results demonstrate that MDU-net significantly outperforms traditional methods and mainstream deep learning models across multiple evaluation metrics. Compared with the classical Dynamic Time Warping (DTW) method, MDU-net improves the Top-10 hit rate by 7.7 percentage points, and by approximately 14.7 percentage points over the Hausdorff distance. In comparisons with deep learning models, the advantage of MDU-net is even more pronounced, it achieves a 25 percentage point improvement in Top-10 hit rate over the Convolutional Autoencoder (CAE), fully validating the superior effectiveness of MDU-net in ship trajectory similarity measurement tasks.