联合TDOA-SA的扫描辐射源半正定松弛定位算法

张海蕊; 张兆林; 谢坚; 陶明亮; 王伶

doi:10.12263/DZXB.20260058

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联合TDOA-SA的扫描辐射源半正定松弛定位算法

学术论文 | 更新时间：2026-06-16

- 联合TDOA-SA的扫描辐射源半正定松弛定位算法
- Semidefinite Relaxation-Based Localization of Scanning Emitters Using Joint SA and TDOA Measurements
- 电子学报 2026年54卷第3期页码：1221-1233
- 作者机构：
  
  西北工业大学电子信息学院，陕西西安 710072
- 作者简介：
  
  张海蕊女，2001年3月出生于河北省定州市。现为西北工业大学电子信息学院硕士研究生。主要研究方向为阵列信号处理、辐射源定位等。E-mail: zhr2001@mail.nwpu.edu.cn
  张兆林男，1978年1月出生于河南省濮阳市。现为西北工业大学电子信息学院副教授、硕士研究生导师。主要研究方向为阵列信号处理、通信抗干扰技术等。E-mail: z184@nwpu.edu.cn
  谢坚男，1986年11月出生于江苏省南通市。现为西北工业大学电子信息学院教授、博士研究生导师。主要研究方向为电子侦察、阵列信号处理、辐射源定位技术等。中国电子学会会员编号：E190020092M。E-mail: xiejian@nwpu.edu.cn
  陶明亮男，1989年8月出生于湖南省株洲市。现为西北工业大学电子信息学院教授、博士研究生导师。主要研究方向雷达信号处理、目标智能探测与侦察等。中国电子学会会员编号：E190014868S。E-mail: mltao@nwpu.edu.cn
  王伶男，1978年10月出生于贵州省仁怀市。现为西北工业大学电子信息学院教授、博士研究生导师。研究方向为通信抗干扰技术、阵列信号处理、导航通信技术等。中国电子学会会员编号：E190014837S。E-mail: lingwang@nwpu.edu.cn
- 基金信息：
  
  国家自然科学基金(62571444;62271412)
- DOI：10.12263/DZXB.20260058
  中图分类号： TN958.7;
- 收稿：2026-02-08，
  
  录用：2026-03-12，
  
  纸质出版：2026-03-25
- 稿件说明：
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张海蕊, 张兆林, 谢坚, 等. 联合TDOA-SA的扫描辐射源半正定松弛定位算法[J]. 电子学报, 2026, 54(03): 1221-1233.

ZHANG Hairui, ZHANG Zhaolin, XIE Jian, et al. Semidefinite Relaxation-Based Localization of Scanning Emitters Using Joint SA and TDOA Measurements[J]. Acta Electronica Sinica, 2026, 54(03): 1221-1233.
张海蕊, 张兆林, 谢坚, 等. 联合TDOA-SA的扫描辐射源半正定松弛定位算法[J]. 电子学报, 2026, 54(03): 1221-1233. DOI：10.12263/DZXB.20260058

ZHANG Hairui, ZHANG Zhaolin, XIE Jian, et al. Semidefinite Relaxation-Based Localization of Scanning Emitters Using Joint SA and TDOA Measurements[J]. Acta Electronica Sinica, 2026, 54(03): 1221-1233. DOI：10.12263/DZXB.20260058

摘要

扫描辐射源因其主瓣信号信噪比高、波束窄、扫描周期稳定等特点，在军事领域和民用领域获得了广泛的应用。针对扫描辐射源无源定位中单一量测体制信息有限的问题，本文提出一种联合时差（Time Difference Of Arrival，TDOA）和扫描角度（Scanning Angle，SA）的半正定松弛扫描辐射源定位算法。首先，构建了联合TDOA-SA的扫描辐射源最大似然定位模型。其次，针对联合体制非凸代价函数存在的初始值敏感、易陷入局部最优的问题，通过引入辅助变量对原始非凸的观测模型进行松弛处理，将问题转化为可高效求解的凸优化形式，从而获得稳定的全局最优解。在此基础上，结合距离二阶锥约束与扫描角度有界约束进行可行域分析，缩小松弛后引起的可行域扩张，实现扫描辐射源的精确定位。最后，进行了联合体制的克拉美罗下界（Cramér-Rao Lower Bound，CRLB）推导和最小观测站数目分析，并通过仿真试验分析所提算法的定位性能。仿真结果表明，在量测误差较大场景下，联合TDOA-SA的定位精度优于单一SA量测定位体制。当扫描角度测量均方根误差小于1°、时差测量均方根误差小于50 µs时，本文所提算法定位精度逼近克拉美罗性能界。

Abstract

Scanning emitters are characterized by high main-lobe signal-to-noise ratios

narrow beams

and stable scan periods

and have been widely deployed in both military and civilian applications. To address the limited information offered by a single measurement modality in passive localization of scanning emitters

this paper proposes a semidefinite-relaxation localization algorithm that jointly exploits time difference of arrival (TDOA) and scanning angle (SA) measurements. We first formulate a maximum-likelihood localization model under the combined TDOA-SA measurement scheme. To overcome the strong nonconvexity of the resulting cost function-manifested by sensitivity to initialization and susceptibility to local minima-we introduce auxiliary variables to relax the original nonconvex observation model and recast the problem into an efficiently solvable convex optimization program

yielding a stable globally optimal solution to the relaxed formulation. On this basis

feasible-set analysis is conducted by incorporating second-order cone constraints on range and bounded constraints on scanning angle

which effectively suppresses the feasible-set expansion induced by relaxation and enables accurate emitter localization. Furthermore

the Cramér-Rao lower bound (CRLB) under the joint measurement scheme is derived

and the minimum number of required receiving stations is analyzed. Simulation studies are conducted to evaluate the localization performance of the proposed algorithm. Simulation results demonstrate that

under scenarios with relatively large measurement errors

the proposed joint TDOA-SA scheme achieves higher localization accuracy than the scheme relying solely on SA measurements. When the root-mean-square error (RMSE) of SA measurement is below 1° and the RMSE of TDOA is below 50 µs

localization performance of the proposed algorithm approaches the CRLB .

关键词

Keywords

references

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