Abstract: The Sparsity Rank Singular Value Decomposition (SRSVD) method and Semi-Exact Augmented Lagrange Multiplier (SEALM) algorithm cannot fit the node trajectory of Wireless Sensor Network (WSN) accurately when the sampling rate is small, the sparse noise is large, and the Gaussian noise exists. In order to solve the problems, a novel Regularized Weighted Incomplete Robust Principal Component Analysis (RWIRPCA) method was proposed. Firstly, the Incomplete Robust Principal Component Analysis (IRPCA) was applied to the fitting of node trajectory. Then, on the basis of IRPCA, in order to better describe the low rank and sparsity of matrices, as well as the anti-Gauss noise performance of enhanced model, the low rank matrix and the sparse matrix were weighted respectively. Finally, the F norm of Gaussian noise matrix was used as a regular term and applied to the fitting of node trajectory. The simulation results show that, the fitting effects of IRPCA and RWIRPCA are better than those of SRSVD and SEALM in the case that the sampling rate is small and the sparse noise is large. Especially, the proposed RWIRPCA can still obtain accurate and stable results when both sparse noise and Gaussian noise exist at the same time.

Key words: Wireless Sensor Network (WSN), Robust Principal Component Analysis (RPCA), Matrix Completion (MC), Weighted Norm (WN), regular term

摘要： 针对稀疏矩阵奇异值分解（SRSVD）方法和半精确增广拉格朗日（SEALM）算法在采样比例小且稀疏噪声大，以及存在高斯噪声时不能准确拟合无线传感器网络（WSN）节点轨迹的问题，提出一种正则化的加权不完全鲁棒主成分分析（RWIRPCA）方法。首先，将不完全鲁棒主成分分析（IRPCA）应用于节点轨迹拟合；然后，在IRPCA的基础上，为了更好地刻画矩阵的低秩性和稀疏性，以及增强模型的抗高斯噪声性能，分别对低秩矩阵和稀疏矩阵进行加权；最后，将高斯噪声矩阵的F范数作为正则项，应用于节点轨迹拟合。仿真结果表明，IRPCA和RWIRPCA在采样比例小且稀疏噪声大时拟合效果均优于SRSVD和SEALM方法，特别是所提的RWIRPCA在稀疏噪声和高斯噪声同时存在时，仍能取得准确且稳定的拟合效果。

关键词: 无线传感器网络, 鲁棒主成分分析, 矩阵补全, 加权范数, 正则项