Semidefinite Relaxation-Based Localization of Scanning Emitters Using Joint SA and TDOA Measurements

ZHANG Hairui; ZHANG Zhaolin; XIE Jian; TAO Mingliang; WANG Ling

doi:10.12263/DZXB.20260058

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Semidefinite Relaxation-Based Localization of Scanning Emitters Using Joint SA and TDOA Measurements

PAPERS | 更新时间：2026-06-16

- Semidefinite Relaxation-Based Localization of Scanning Emitters Using Joint SA and TDOA Measurements
- ACTA ELECTRONICA SINICA Vol. 54, Issue 3, Pages: 1221-1233(2026)
- 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：
- 基金信息：
  
  National Natural Science Foundation of China(62571444;62271412)
- DOI：10.12263/DZXB.20260058
  CLC： TN958.7;
- Received：08 February 2026，
  
  Accepted：12 March 2026，
  
  Published：25 March 2026
- 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

郭福成 , 李金洲 , 张敏 . 无源定位原理与方法 [M ] . 北京 : 国防工业出版社 , 2021 .

Guo Fucheng , Li Jinzhou , Zhang Min . Passive location theories and methods [M ] . Beijing : National Defense Industry Press , 2021 . (in Chinese)

Sun Yimao , Ho K C , Wan Qun . Eigenspace solution for AOA localization in modified polar representation [J ] . IEEE Transactions on Signal Processing , 2020 , 68 : 2256 - 2271 . DOI: 10.1109/tsp.2020.2981773 http://dx.doi.org/10.1109/tsp.2020.2981773

汤新民 , 周杨 , 鲁其兴 , 等 . 基于信号到达时间建模的广域多点定位时间同步方法 [J ] . 电子与信息学报 , 2025 , 47 ( 5 ): 1434 - 1449 . DOI: 10.11999/JEIT240670 http://dx.doi.org/10.11999/JEIT240670

Tang Xinmin , Zhou Yang , Lu Qixing , et al . Wide-Area multilateration time synchronization method based on signal arrival time modeling [J ] . Journal of Electronics & Information Technology , 2025 , 47 ( 5 ): 1434 - 1449 . (in Chinese) . DOI: 10.11999/JEIT240670 http://dx.doi.org/10.11999/JEIT240670

Sun Yimao , Ho K C , Xing Tianyi , et al . Projection-based algorithm and performance analysis for TDOA localization in MPR [J ] . IEEE Transactions on Signal Processing , 2024 , 72 : 896 - 911 . DOI: 10.1109/tsp.2024.3352923 http://dx.doi.org/10.1109/tsp.2024.3352923

Wang Gang , Yang Shuli , Pei Jian , et al . Bias-reduced SDR method for locating a noncooperative moving source using TOAs and FOAs [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2024 , 60 ( 5 ): 6146 - 6162 . DOI: 10.1109/taes.2024.3403070 http://dx.doi.org/10.1109/taes.2024.3403070

关浩亮 , 张顺生 , 王文钦 . 基于频控阵的无源定位对抗技术 [J ] . 雷达学报 , 2021 , 10 ( 6 ): 833 - 841 . DOI: 10.12000/JR21091 http://dx.doi.org/10.12000/JR21091

Guan Haoliang , Zhang Shunsheng , Wang Wenqin . Passive localization countermeasure based on frequency diverse array [J ] . Journal of Radars , 2021 , 10 ( 6 ): 833 - 841 . (in Chinese) . DOI: 10.12000/JR21091 http://dx.doi.org/10.12000/JR21091

谌东 , 鄢勃 , 贾朝文 , 等 . 浅析机载有源相控阵雷达的特点及对抗技术 [J ] . 电子信息对抗技术 , 2022 , 37 ( 3 ): 95 - 100 . DOI: 10.3969/j.issn.1674-2230.2022.03.019 http://dx.doi.org/10.3969/j.issn.1674-2230.2022.03.019

Chen Dong , Yan Bo , Jia Chaowen , et al . Brief analysis of characteristics and countermeasure technology for airborne active phase array radar [J ] . Electronic Information Warfare Technology , 2022 , 37 ( 3 ): 95 - 100 . (in Chinese) . DOI: 10.3969/j.issn.1674-2230.2022.03.019 http://dx.doi.org/10.3969/j.issn.1674-2230.2022.03.019

Zhang Guangbin , Liu Hengyan , Dai Wei , et al . Passive joint emitter localization with sensor self-calibration [J ] . Remote Sensing , 2023 , 15 ( 3 ): 671 . DOI: 10.3390/rs15030671 http://dx.doi.org/10.3390/rs15030671

Zhang Yifei , Zhang Min , Guo Fucheng . Recursive instrumental variable method for locating a scanning emitter by a single observer using time of interception [J ] . IET Radar , Sonar & Navigation, 2017 , 11 ( 12 ): 1839 - 1844 . DOI: 10.1049/iet-rsn.2017.0097 http://dx.doi.org/10.1049/iet-rsn.2017.0097

Merlo J M , Mghabghab S R , Nanzer J A . Wireless picosecond time synchronization for distributed antenna arrays [J ] . IEEE Transactions on Microwave Theory and Techniques , 2023 , 71 ( 4 ): 1720 - 1731 . DOI: 10.1109/tmtt.2022.3227878 http://dx.doi.org/10.1109/tmtt.2022.3227878

Xin Jihao , Ge Xuyang , Zhang Yuan , et al . High-precision time difference of arrival estimation method based on phase measurement [J ] . Remote Sensing , 2024 , 16 ( 7 ): 1197 . DOI: 10.3390/rs16071197 http://dx.doi.org/10.3390/rs16071197

Hmam H . Scan-based emitter passive localization [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2007 , 43 ( 1 ): 36 - 54 . DOI: 10.1109/taes.2007.357153 http://dx.doi.org/10.1109/taes.2007.357153

Li Wanchun , Li Yingxiang , Wei Ping , et al . A closed-form localization algorithm using angle-of-arrival and difference time of scan time measurements in scan-based radar [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2019 , 55 ( 1 ): 511 - 515 . DOI: 10.1109/TAES.2018.2890353 http://dx.doi.org/10.1109/TAES.2018.2890353

张翼飞 , 张敏 , 郭福成 . 基于DOA和TDOI的主瓣扫描辐射源定位方法 [J ] . 电子与信息学报 , 2017 , 39 ( 12 ): 2921 - 2928 . DOI: 10.11999/JEIT170141 http://dx.doi.org/10.11999/JEIT170141

Zhang Yifei , Zhang Min , Guo Fucheng . Scanning emitter localization using DOA and TDOI measurements [J ] . Journal of Electronics & Information Technology , 2017 , 39 ( 12 ): 2921 - 2928 . (in Chinese) . DOI: 10.11999/JEIT170141 http://dx.doi.org/10.11999/JEIT170141

何友 , 孙顺 , 董凯 , 等 . 扫描辐射源的最大似然定位算法 [J ] . 控制与决策 , 2017 , 32 ( 7 ): 1293 - 1300 . DOI: 10.13195/j.kzyjc.2016.0797 http://dx.doi.org/10.13195/j.kzyjc.2016.0797

He You , Sun Shun , Dong Kai , et al . Maximum likelihood algorithm for scan-based emitter localization [J ] . Control and Decision , 2017 , 32 ( 7 ): 1293 - 1300 . (in Chinese) . DOI: 10.13195/j.kzyjc.2016.0797 http://dx.doi.org/10.13195/j.kzyjc.2016.0797

Li Wanchun , Wang Li , Yang Tianliu , et al . Joint scan rate and emitter location estimation algorithm in SBR system based on AOA and DTOST measurements [J ] . IEEE Access , 2020 , 8 : 66598 - 66608 . DOI: 10.1109/ACCESS.2020.2985068 http://dx.doi.org/10.1109/ACCESS.2020.2985068

邓兵 , 姚山峰 , 杨宇翔 , 等 . 到达时间差与扫描时间差定位精度分析 [J ] . 兵器装备工程学报 , 2024 , 45 ( 1 ): 249 - 255 . DOI: 10.11809/bqzbgcxb2024.01.033 http://dx.doi.org/10.11809/bqzbgcxb2024.01.033

Deng Bing , Yao Shanfeng , Yang Yuxiang , et al . Precision analysis for TDOA-TDOS localization [J ] . Journal of Ordnance Equipment Engineering , 2024 , 45 ( 1 ): 249 - 255 . (in Chinese) . DOI: 10.11809/bqzbgcxb2024.01.033 http://dx.doi.org/10.11809/bqzbgcxb2024.01.033

杨静 , 刘成城 , 黄洁 , 等 . 联合时延-多普勒-角度的无源雷达目标定位凸优化算法 [J ] . 电子学报 , 2024 , 52 ( 6 ): 2091 - 2102 .

Yang Jing , Liu Chengcheng , Huang Jie , et al . Convex solution for target localization in passive MIMO radar using delay, doppler and angle measurements [J ] . Acta Electronica Sinica , 2024 , 52 ( 6 ): 2091 - 2102 . (in Chinese)

Wang Yiqiu , Tao Meixia , Sun Shu . Cramér-Rao bound analysis and beamforming design for integrated sensing and communication with extended targets [J ] . IEEE Transactions on Wireless Communications , 2024 , 23 ( 11 ): 15987 - 16000 . DOI: 10.1109/twc.2024.3435864 http://dx.doi.org/10.1109/twc.2024.3435864

Singh K , Makarim A F , Albinsaid H , et al . Passive beamforming design and DNN-based signal detection in RIS-assisted MIMO systems with generalized spatial modulation [J ] . IEEE Transactions on Vehicular Technology , 2023 , 72 ( 2 ): 1879 - 1892 . DOI: 10.1109/tvt.2022.3208830 http://dx.doi.org/10.1109/tvt.2022.3208830

秦兆涛 , 王俊 , 魏少明 , 等 . 基于目标高度先验信息的多站时差无源定位方法 [J ] . 电子与信息学报 , 2018 , 40 ( 9 ): 2219 - 2226 . DOI: 10.11999/JEIT171231 http://dx.doi.org/10.11999/JEIT171231

Qin Zhaotao , Wang Jun , Wei Shaoming , et al . Passive localization using TDOA measurements from multiple sensors based on priori knowledge of target altitude [J ] . Journal of Electronics & Information Technology , 2018 , 40 ( 9 ): 2219 - 2226 . (in Chinese) . DOI: 10.11999/JEIT171231 http://dx.doi.org/10.11999/JEIT171231

Zhou Qiyu , Yuan Ye , Venturino L , et al . Direct target localization for distributed passive radars with direct-path interference suppression [J ] . IEEE Transactions on Signal Processing , 2024 , 72 : 3611 - 3625 . DOI: 10.1109/tsp.2024.3414423 http://dx.doi.org/10.1109/tsp.2024.3414423

Li Jiaqi , Dong Xudong , Shi Xinlei , et al . An enhanced direct position determination of non-circular sources via sparse Bayesian inference and grid refinement strategy [J ] . Digital Signal Processing , 2024 , 151 : 104564 . DOI: 10.1016/j.dsp.2024.104564 http://dx.doi.org/10.1016/j.dsp.2024.104564

Bianco G M , Giuliano R , Mazzenga F , et al . Multi-slope path loss and position estimation with grid search and experimental results [J ] . IEEE Transactions on Signal and Information Processing over Networks , 2021 , 7 : 551 - 561 . DO I: 10.1109/tsipn.2021.3106693 http://dx.doi.org/10.1109/tsipn.2021.3106693

Wang Gang , Xiao Yudong , Ho K C , et al . Unified near-field and far-field TDOA source localization without the knowledge of signal propagation speed [J ] . IEEE Transactions on Communications , 2024 , 72 ( 4 ): 2166 - 2181 . DOI: 10.1109/tcomm.2023.3342228 http://dx.doi.org/10.1109/tcomm.2023.3342228

Dai Zichao , Wang Gang , Chen Hongyang . Sensor selection for TDOA-based source localization using angle and range information [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2021 , 57 ( 4 ): 2597 - 2604 . DOI: 10.1109/TAES.2021.3061826 http://dx.doi.org/10.1109/TAES.2021.3061826

Luo Zhiquan , Ma W K , So A M C , et al . Semidefinite relaxation of quadratic optimization problems [J ] . IEEE Signal Processing Magazine , 2010 , 27 ( 3 ): 20 - 34 . DOI: 10.1109/msp.2010.936019 http://dx.doi.org/10.1109/msp.2010.936019

Jiao Xiaoshuang , Chen Jinming , Jiang Lifeng , et al . A distributed low-degree-of-freedom aerial target localization method based on hybrid measurements [J ] . Remote Sensing , 2025 , 17 ( 10 ): 1705 . DOI: 10.3390/rs17101705 http://dx.doi.org/10.3390/rs17101705

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