Xu Pengfei, Cui Tianhao, Chen Lei
School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China.
Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing University of Posts &Telecommunications, Nanjing 210023, China.
Sensors (Basel). 2019 Apr 23;19(8):1912. doi: 10.3390/s19081912.
Accurate and sufficient node location information is crucial for Wireless Sensor Networks (WSNs) applications. However, the existing range-based localization methods often suffer from incomplete and detorted range measurements. To address this issue, some methods based on low-rank matrix recovery have been proposed, which usually assume noises follow single Gaussian distribution or/and single Laplacian distribution, and thus cannot handle the case with wider noise distributions beyond Gaussian and Laplacian ones. In this paper, a novel Anomaly-aware Node Localization (ANLoC) method is proposed to simultaneously impute missing range measurements and detect node anomaly in complex environments. Specifically, by utilizing inherent low-rank property of Euclidean Distance Matrix (EDM), we formulate range measurements imputation problem as a Robust ℓ 2 , 1 -norm Regularized Matrix Decomposition (RRMD) model, where complex noise is fitted by Mixture of Gaussian (MoG) distribution, and node anomaly is sifted by ℓ 2 , 1 -norm regularization. Meanwhile, an efficient optimization algorithm is designed to solve proposed RRMD model based on Expectation Maximization (EM) method. Furthermore, with the imputed EDM, all unknown nodes can be easily positioned by using Multi-Dimensional Scaling (MDS) method. Finally, some experiments are designed to evaluate performance of the proposed method, and experimental results demonstrate that our method outperforms three state-of-the-art node localization methods.
准确且充分的节点位置信息对于无线传感器网络（WSN）应用至关重要。然而，现有的基于距离的定位方法常常受到不完整和扭曲的距离测量的困扰。为了解决这个问题，已经提出了一些基于低秩矩阵恢复的方法，这些方法通常假设噪声服从单一高斯分布或/和单一拉普拉斯分布，因此无法处理高斯和拉普拉斯分布之外更广泛噪声分布的情况。本文提出了一种新颖的异常感知节点定位（ANLoC）方法，以在复杂环境中同时插补缺失的距离测量并检测节点异常。具体而言，通过利用欧几里得距离矩阵（EDM）固有的低秩特性，我们将距离测量插补问题表述为一个鲁棒的ℓ2,1范数正则化矩阵分解（RRMD）模型，其中复杂噪声由高斯混合（MoG）分布拟合，节点异常通过ℓ2,1范数正则化进行筛选。同时，设计了一种高效的优化算法，基于期望最大化（EM）方法求解所提出的RRMD模型。此外，利用插补后的EDM，所有未知节点都可以通过使用多维缩放（MDS）方法轻松定位。最后，设计了一些实验来评估所提出方法的性能，实验结果表明我们的方法优于三种现有的节点定位方法。
