一种利用半正定松弛的运动目标无源定位算法  

Semidefinite relax method for moving targets localization

作　　者：周成[1] 林茜[1] 马丛珊 应涛[1] 满欣[1] ZHOU Cheng;LIN Qian;MA Congshan;YING Tao;MAN Xin(College of Electronic Engineering,Naval University of Engineering,Wuhan 430033,China)

机构地区：[1]海军工程大学电子工程学院,湖北武汉430033

出　　处：《西安电子科技大学学报》2025年第1期94-104,共11页Journal of Xidian University

基　　金：国家自然科学基金(61501484);湖北省自然科学基金(2023AFB1039)。

摘　　要：利用多个接收站测量得到的目标辐射源信号到达时差、到达频差和差分多普勒率信息进行联合定位,可以有效提高运动目标的无源定位精度,是当前研究的热点。但是,现有算法通常采用两步加权最小二乘方法,在低信噪比环境下普遍存在定位误差较大的问题。为了解决该问题,通过将无源定位问题逐步转化为凸优化问题,采用成熟的凸优化技术,提出了一种基于半正定松弛的运动目标无源定位算法。该方法分为三步:第一步,通过引入三个辅助变量,构建伪线性的无源定位方程组;第二步,利用辅助变量与目标定位解之间的关系,将定位问题转化为具有二次约束的二次规划问题;第三步,采用半正定松弛方法,将二次约束优化转为凸优化问题,并运用优化工具箱高效求解。仿真结果表明:与现有方法相比,所提算法目标定位精度达到克拉美罗界所需信噪比至少降低9 dB,且在更低的信噪比环境下具有更小的定位误差。证明了所提算法的有效性。Using the time difference of arrival,frequency difference of arrival,and differential Doppler rate measurements from target radiation signals received by multiple receivers for joint localization is a current research hotspot as it can effectively enhance the passive location accuracy of moving targets.However,existing algorithms commonly employ a two-step weighted least squares method,which often results in significant positioning errors in low signal-to-noise ratio environments.To address this issue,a semidefinite relax method for moving targets localization is proposed.This method en-compasses three steps:first,by introducing three auxiliary variables,a pseudolinear passive location equation set is constructed;second,the localization problem is transformed into a quadratic pro-gramming problem with quadratic constraints by leveraging the relationship between the auxiliary variables and the target localization solution;finally,the semidefinite relaxation method is employed to convert the quadratic constraint optimization into a convex optimization problem,which is efficiently solved using optimization toolboxes.Simulation results demonstrate that,compared with the existing methods,the signal-to-noise ratio required by the proposed algorithm to achieve the target localization accuracy of the Cramer-Rao Lower Bound is smaller by at least 9 dB,and the proposed algorithm has a smaller localization error in lower signal-to-noise ratio environment.The effectiveness of the pro-posed algorithm is proved.

关 键 词：无源定位 到达时差 到达频差 差分多普勒率 半正定松弛 

分 类 号：TN97[电子电信—信号与信息处理]