基于秩最小化矩阵去噪的船舶轨迹重构方法

针对船舶自动识别系统(Automatic Identification System，AIS)在实际应用中存在错误数据频发、数据丢包等问题，本文提出一种基于秩最小化矩阵去噪的船舶轨迹重构方法，利用去噪实现轨迹重构，同时，实现对轨迹的去噪和缺失补全。该方法通过线性插值实现经度对齐，将轨迹数据转化为轨迹矩阵，从而补全轨迹中的缺失值。由于补全结果存在非常大的误差，因此，引入 PLR(Patch-Based Low-Rank Minimization)算法去噪，消除误差。同时，为进一步提升补全效果，通 过2D-VMD(Two-Dimensional Variational Mode Decomposition)算法将矩阵分解为不同频率的IMF (Intrinsic Mode Function)，并分别进行PLR去噪，合并去噪结果，得到最终重构后轨迹。本文以长江武汉段水域船舶AIS轨迹为研究对象，通过实验证明该方法在不同缺失比例以及随机缺失和连续缺失两种情境下具有鲁棒性和较强的稳定性；并与 HALRTC(High-Accuracy Low-Rank Tensor Completion)、TRMF(Temporal Regularized Matrix Factorization)等方法进行比较，结果表明， 该方法相较于HALRTC等方法具有更高的精度，并在高损失率下表现出较好的重构效果。

A Vessel Trajectory Reconstruction Method Based on Low-rank Minimization Matrix Denoising

The operation of (Automatic Identification System) AIS shows some frequent error data and missing data. This paper proposes a vessel trajectory reconstruction method based on low-rank minimization matrix denoising. This method realizes the trajectory reconstruction by denoising and the trajectory denosing and missing data become complete through a union method. In this method, the trajectory matrix is constructed and the corresponding longitudes of the points in the same column are ensured to be the same via linear interpolation to complete the missing values in the trajectories. Due to the large error in the completion results, the PLR (Patch-Based Low-Rank Minimization) algorithm is used to denoise and reduce bias. To further improve the completion effect, the trajectory matrix is decomposed into the IMFs (Intrinsic Mode Functions) with different frequencies by the 2D-VMD (Two-Dimensional Variational Mode Decomposition) and then denoised by the PLR algorithm. The reconstructed trajectories were obtained by combining the denoising results. The trajectories in the AIS of Wuhan section of Yangtze River were studied as an example. This method is robust and stable to the trajectories with different missing rate under two missing scenarios: random missing and continuous missing. In addition, the proposed method is tested and compared with the High- Accuracy Low- Rank Tensor Completion (HALRTC) Temporal Regularized Matrix Factorization (TRMF) and other methods. The results show the proposed method has higher accuracy especially when the trajectories have a high missing rate.