一种基于凸优化的四站时差定位算法  

Four-station time difference positioning algorithm based on convex optimization

作　　者：张欢 周云生 姜义成[2] ZHANG Huan;ZHOU Yunsheng;JIANG Yicheng(Beijing Research Institute of Telemetry,Beijing 100094,China;School of Electronics and Information Engineering,Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]北京遥测技术研究所,北京100094 [2]哈尔滨工业大学电子与信息工程学院,黑龙江哈尔滨150001

出　　处：《应用科技》2021年第1期76-80,共5页Applied Science and Technology

摘　　要：在多站无源时差定位问题中,观测站运动使自身位置信息存在位置误差,由于定位误差的存在,传统时差定位算法定位精度不能满足高精度辐射源定位的要求。针对这一问题,提出一种基于凸优化的时差定位算法,以四站时差定位系统为例,对地球表面的辐射源进行定位。首先在WGS-84模型下,给出存在位置误差时的时差定位方程,通过引入中间变量并对时差定位方程进行松弛变换,将非线性的时差定位方程转换成一个凸优化问题,利用MATLAB中成熟的CVX工具箱可以有效求解得到辐射源位置坐标。仿真结果表明:与传统时差定位方法相比,本文算法在相同时差测量误差或位置误差条件下的定位误差更小,通过对多次定位结果进行卡尔曼滤波处理进一步提升了辐射源定位精度。In the problem of multi-station passive time difference positioning,the movement of the observing station results in position error in its own position information.Due to the existence of positioning error,the positioning accuracy of traditional time difference positioning algorithms cannot meet the requirements of high-precision radiation source positioning.In order to solve this problem,a time difference positioning algorithm is proposed in this paper based on convex optimization.Taking a four-station time difference positioning system as an example,the radiation source on the surface of the earth is located.Firstly,the time difference positioning equation with position error is given under the WGS-84 model.Then,by introducing intermediate variables and performing a relaxation transformation on the time difference positioning equation,the nonlinear time difference positioning equation is converted into a convex optimization problem.Finally,the CVX toolbox in Matlab can effectively solve the problem and the radiation source position coordinates are obtained.The simulation results show that the positioning error of the algorithm proposed in this paper is smaller than that of the traditional time difference positioning method under the condition of same time difference measurement error or position error.The Kalman filter processing of multiple positioning results further improves the positioning accuracy of the radiation source.

关 键 词：无源定位 四站时差定位系统 地面辐射源 定位算法 WGS-84模型 凸优化 CVX 定位精度 

分 类 号：TN971[电子电信—信号与信息处理]