基于低秩逼近的无线传感网定位算法  

Sensor network localization using low-rank approximation

作　　者：诸一琦 诸燕平[2] 张景林 陈瑞 Zhu Yiqi;Zhu Yanping;Zhang Jinglin;Chen Rui(School of Electrical and Information Engineering,Jiangsu University of Technology,Changzhou 213001,China;School of Microelectronics and Control Engineering,Changzhou University,Changzhou 213164,China)

机构地区：[1]江苏理工学院电气信息工程学院,常州213001 [2]常州大学微电子与控制工程学院,常州213164

出　　处：《电子测量技术》2022年第23期147-152,共6页Electronic Measurement Technology

基　　金：江苏省重点研发专项资金(现代农业)项目(BE2019317);国家自然科学基金青年科学基金(61801055)项目资助。

摘　　要：为了提高传感网节点定位精度并降低运算量,提出一种新的基于低秩逼近的定位算法。算法首先获取邻居节点间距离测量值,然后填充欧氏距离矩阵,最后通过对锚节点坐标进行刚性变换得到未知节点坐标。为了更准确地填充距离矩阵,根据格拉姆矩阵的低秩特性将定位问题转化为半定规划问题,并在定位模型中引入正则化项来避免填充欧氏距离矩阵时的退化解问题。针对半定规划求解复杂度高的缺点,采用交替方向乘子法来更快地求解。通过仿真实验对比,在大噪声情况下,本算法相较于传统算法(包括多维缩放法和其他欧式距离填充算法),均方根误差减小28.2%~46.6%,重建误差减小18.4%~64.5%;计算时间仅需SDP算法的7%。To improve the localization accuracy of sensor network nodes and reduce the computational workload, a novel algorithm based on low-rank approximation was proposed. Given distance measurements obtained between sensors in the neighborhood, the proposed algorithm first fulfilled the Euclidean distance matrix(EDM) completion. Then, sensors’ positions were obtained by rigid transformation using anchors’ positions. To achieve accurate range information, the EDM completion stage exploited the low-rank essence of the Gram matrix of sensors’ coordinate matrix, resulting in a semidefinite programming(SDP) problem. Furthermore, some regularization term was introduced in our localization model to avoid degenerate solutions in the EDM completion stage. In practice, solving a large-scale SDP problem is still a challenging task. To improve the scalability of the proposed algorithm, an alternating direction method of multipliers(ADMM) was further developed. Compared with traditional algorithms(including multidimensional scaling method and other Euclidean distance-filling algorithms), this algorithm reduces the root mean square error by 28.2%~46.6% and the reconstruction error by 18.4%~64.5% in the case of large noise through simulation experiments, and the computation time is only 7% of that of SDP algorithm.

关 键 词：欧氏距离矩阵 低秩 半定规划 交替方向乘子法 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]