WGS-84模型下时差频差半定规划定位算法

doi:10.7527/S1000-6893.2017.320843

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WGS-84模型下时差频差半定规划定位算法

李万春^1,2, 彭吴可^1,3, 彭丽¹, 马叶子¹, 李英祥²

1. 电子科技大学电子工程学院网络空间安全研究中心, 成都 611731;
2. 成都信息工程大学通信工程学院气象信息与信号处理四川省高校重点实验室, 成都 610225;
3. 清华大学医学院, 北京 100084

收稿日期:2016-10-12 修回日期:2016-11-28 出版日期:2017-07-15 发布日期:2017-04-01
通讯作者: 李万春,E-mail:liwanchun@uestc.edu.cn E-mail:liwanchun@uestc.edu.cn
基金资助:
气象信息与信号处理四川省高校重点实验室基金

Semidefinite programming algorithm with TDOA and FDOA measurements based on WGS-84 earth model

LI Wanchun^1,2, PENG Wuke^1,3, PENG Li¹, MA Yezi¹, LI Yingxiang²

1. Center for Cyber Security, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. Meteorological Information and Signal Processing Key Laboratory of Sichuan Higher Education Institutes, School of Communication Engineering, Chengdu University of Information Technology, Chengdu 610225, China;
3. School of Medicine, Tsinghua University, Beijing 100084, China

Received:2016-10-12 Revised:2016-11-28 Online:2017-07-15 Published:2017-04-01
Supported by:
Meteorological Information and Signal Processing Key Laboratory of Sichuan Higher Education Institutes

摘要/Abstract

摘要：

利用多颗卫星的时差频差对辐射源进行位置和速度的测量，其本质意义上是一个含有噪声项的高度非线性方程组求解问题，针对地面目标而言，可以采用基于WGS-84地球模型作为目标位置和速度约束，更进一步的增加了定位系统的复杂性。提出了一种基于半定规划（SDP）的定位解算法，将非线性方程求解问题通过适当的松弛，转化为半定优化（SDO）的问题，借助于业界较为成熟的CVX等优化软件进行定位求解，并研究了该模型条件下的克拉美罗下界（CRLB）。仿真结果表明，该算法能够较好地逼近克拉美罗下界。

关键词: WGS-84模型, 时差定位, 频差定位, 半定规划, 克拉美罗下界

Abstract:

In essence, detecting the location and velocity of a radiation source by utilizing time difference of arrival/frequency difference of arrival (TDOA/FDOA) for multiple satellites can be deemed as a highly nonlinear solution problem within noise. For a ground target, the WGS-84 earth model is the constraint condition, which makes the location system become more complicated. In this paper, a new algorithm for solving this location problem is proposed based on the semi-definite programming (SDP). Based on the novel algorithm, the nonlinear location problem can turn into a semidefinite optimization (SDO) by an appropriate relaxation which can be solved by some mature software like CVX. According to this model, the Cramer-Rao Lower Bound (CRLB) of the location problem is then given. The computer simulation demonstrates that the proposed algorithm can approach the CRLB effectively.

Key words: WGS-84 earth model, location by time difference of arrival, location by frequency difference of arrival, semidefinite programming, Cramer-Rao lower bound

中图分类号:

V19
TN967.1

李万春, 彭吴可, 彭丽, 马叶子, 李英祥. WGS-84模型下时差频差半定规划定位算法[J]. 航空学报, 2017, 38(7): 320843-320843.

LI Wanchun, PENG Wuke, PENG Li, MA Yezi, LI Yingxiang. Semidefinite programming algorithm with TDOA and FDOA measurements based on WGS-84 earth model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(7): 320843-320843.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

WGS-84模型下时差频差半定规划定位算法

Semidefinite programming algorithm with TDOA and FDOA measurements based on WGS-84 earth model

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