基于半定松弛优化估计的无线传感网络定位  

Positioning of Wireless Sensor Networks Based on Semidefinite Relaxation Optimization

作　　者：李晓飞 陈广福 蓝天明 LI Xiaofei;CHEN Guangfu;LAN Tianming(Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry,Wuyishan 354300 China;College of Mathematics and Computer,Wuyi University,Wuyishan 354300 China)

机构地区：[1]茶产业大数据应用与智能化重点实验室,福建武夷山354300 [2]武夷学院数学与计算机学院,福建武夷山354300

出　　处：《西华大学学报（自然科学版）》2023年第1期66-72,99,共8页Journal of Xihua University:Natural Science Edition

基　　金：福建省自然科学基金项目(2021J011142,2021J011146,2021J011147);南平市科技计划项目(N2021J007)。

摘　　要：针对复杂环境下的无线传感节点位置定位精度的问题,提出一种基于无迹卡尔曼滤波的半定松弛优化估计(SC-SDP)算法,以实现无线传感器网络中节点位置的准确估计。文章基于半定松弛优化估计定位技术,建立系统模型并将其作为一个优化问题,通过寻找初始非凸目标函数的更低下界来重新阐述优化问题,将非线性和非凸问题分别松弛优化,得到次优化解;采用无迹卡尔曼算法过滤其噪声,获得一个可更准确地捕捉真实均值和协方差的滤波器,并且利用无轨迹转换使高斯输入信号精确到三阶,非高斯输入信号精确到二阶。大量的实验结果分析表明:SC-SDP算法在无线传感器网络的定位误差(RMSE)要优于GM-SDP算法、WLS算法以及CRLB算法的定位误差,提高了无线传感器网络的定位精度;半定松弛化算法的抗干扰性得到改善。Aiming at the problem of positioning accuracy analysis of wireless sensor nodes in complex environments, the semi-definite relaxation optimization estimation algorithm based on the Kalman filter(SC-SDP) is proposed to achieve the accurate estimation of the node position in a wireless sensor network. This paper proposes a positioning technology based on semi-definite relaxation optimization estimation, establishes a system model and asks questions, and re-elaborates the optimization problem by finding the lower bound of the initial non-convex objective function. The nonlinear and nonconvex problems are relaxed and optimized separately, and suboptimal solutions are obtained. The unscented Kalman algorithm is used to filter the noise, and a filter that captures the true mean and covariance more accurately is obtained in the paper. The traceless transformation can make the Gaussian inputting signal accurate to the third order,and the non-Gaussian inputting signal to the second order. The experimental results show that the positioning root mean square error(RMSE) of the sensor complex network using semidefinite relaxation optimization( SC-SDP) algorithm in the wireless sensor network is better than the positioning root mean square error(RMSE) of the Gaussian mixture model via semidefinite relaxation(GM-SDP)、weighed least msquares(WLS) and cramer-rao lower(CRLB), and the accuracy is higher than other algorithms, which improves the wireless sensor network. The positioning accuracy and anti-interference performance of the wireless sensor network are improved, and the noise and positioning error are alleviated, and the performance of the semidefinite relaxation algorithm is improved to a certain extent.

关 键 词：半定松弛化 定位精度 噪声过滤 非线性 非凸性 

分 类 号：TP212.9[自动化与计算机技术—检测技术与自动化装置] TN929.5[自动化与计算机技术—控制科学与工程]