基于Bregman散度的无线传感器网络定位

现有算法难以处理脉冲噪声，导致无线传感器网络（WSN）中节点定位精度较低，为此提出基于Bregman散度的WSN定位算法. 该算法分为2个阶段：欧氏距离矩阵（EDM）恢复阶段和坐标映射阶段. 基于EDM的自然低秩性，将EDM恢复问题转化为噪声环境下的矩阵补全问题；采用L_1，2范数显式平滑脉冲噪声，建立正则化矩阵补全模型；为了有效求解该模型，定义多元函数Bregman散度，将分裂Bregman迭代拓展到矩阵空间，结合交替最小化算法，得到EDM的估计；在此基础上，基于多维标度法对节点位置进行估计. 实验结果表明，在不同噪声条件下，该算法在保证高效性的同时，在定位精度和鲁棒性方面优于其他算法，特别是当采样率达到一定程度时，定位误差不到其他算法的1/4.

Wireless sensor network localization via Bregman divergence

The impulse noise is difficult to deal with by using the existing algorithms. A WSN localization algorithm based on the Bregman divergence was proposed to improve the node positioning accuracy of the wireless sensor network (WSN). The proposed algorithm is divided into two stages, the stage of Euclidean distance matrix (EDM) recovery and the stage of coordinates mapping. The problem of EDM recovery is transformed to an issue of matrix completion in a noisy environment, based on the natural low-rank character of the EDM. A regularized matrix completion model is established by using L_1,2-norm explicit smoothing the pulse noise. To solve the model effectively, the multivariate function Bregman divergence was defined, then the split Bregman iteration was extended to the matrix space, and the alternating minimization method was combined to obtain the EDM estimator. Furthermore, node localization was available based on the multi-dimensional scaling method. Experiments demonstrate that under different noise conditions, the proposed algorithm outperforms other algorithms in terms of positioning accuracy and robustness while ensuring high efficiency. Notably, the localization error of the proposed algorithm was less than a quarter of those of other algorithms, when the sampling rate reached a certain level.