基于差分进化算法的多基地声纳目标定位

doi:10.12305/j.issn.1001-506X.2026.06.04

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (6): 1819-1829.doi: 10.12305/j.issn.1001-506X.2026.06.04

基于差分进化算法的多基地声纳目标定位

韦强强¹(), 许林周¹^,*(), 韩东²(), 郭雨桐³()

1. 海军大连舰艇学院水武与防化系，辽宁大连 116018
2. 海军大连舰艇学院信息系统系，辽宁大连 116018
3. 国防科技大学气象海洋学院，湖南长沙 410073

收稿日期:2025-04-24 修回日期:2025-07-27 出版日期:2026-06-25 发布日期:2025-12-08
通讯作者: 许林周 E-mail:9154657@qq.com;xubigboy@163.com;332548360@qq.com;guoyutong@nudt.edu.cn
作者简介:韦强强（1996—），男，硕士研究生，主要研究方向为水声信号处理、飞行航路规划
韩　东（1978—），男，教授，博士研究生导师，博士，主要研究方向为水下通信、水声学
郭雨桐（1995—），女，博士研究生，主要研究方向为海洋环境、大气科学
基金资助:
国家自然科学基金（62371464）资助课题

Target localization for multi-static sonar based on differential evolution algorithm

Qiangqiang WEI¹(), Linzhou XU¹^,*(), Dong HAN²(), Yutong GUO³()

1. Department of Underwater Weaponry and Chemical Defense，Dalian Naval Academy，Dalian 116018，China
2. Department of Information System，Dalian Naval Academy，Dalian 116018，China
3. College of Meteorology and Oceanography，National University of Defense Technology，Changsha 410073，China

Received:2025-04-24 Revised:2025-07-27 Online:2026-06-25 Published:2025-12-08
Contact: Linzhou XU E-mail:9154657@qq.com;xubigboy@163.com;332548360@qq.com;guoyutong@nudt.edu.cn

摘要/Abstract

摘要：

针对复杂噪声条件下传统闭式解算法和部分优化算法在进行多基地声纳目标定位时定位精度和稳定性不足的问题，引入差分进化算法求解定位模型。通过解析信号传输路径的几何关系，建立基于到达时间差的双曲定位模型，并详细阐述差分进化算法求解定位模型的核心思路与数学过程。利用仿真实验，确定适用于不同噪声水平的差分进化算法关键参数；验证在传感器位置、声速、时延测量误差的噪声条件下相较于模拟退火算法和牛顿迭代算法，该算法具备更优的定位性能；并研究定位误差的空间分布特性，尽管从传感器网络的几何中心向外，该算法的定位精度逐渐降低，但仍能实现对目标的有效定位。研究成果证明了差分进化算法在多基地声纳系统中进行目标定位的可行性和鲁棒性。

关键词: 差分进化算法, 多基地声纳, 到达时间差, 目标定位

Abstract:

To address the insufficient localization accuracy and stability of traditional closed-form solutions and part optimization algorithms in multi-static sonar target localization with complex noise conditions, the differential evolution （DE） algorithm is employed in this study to solve the localization model. By analyzing the geometric relationships of signal transmission paths, a hyperbolic localization model based on time difference of arrival is established, and the core idea and mathematical procedures of solving the localization model using the DE algorithm are elaborated in detail. Simulation experiments are conducted to determine the key DE algorithm parameters suitable for various noise levels. The results validate that with conditions involving sensor-position, sound-speed, and time-delay measurement errors, the DE algorithm achieves superior localization performance compared to both the simulated annealing algorithm and the Newton iteration method. Moreover, the spatial distribution characteristics of localization errors are investigated. Although the localization accuracy gradually decreases with increasing distance from the geometric center of the sensor network, the algorithm remains effective in achieving target localization. The research demonstrates the feasibility and robustness of applying the DE algorithm for target localization in multi-static sonar systems.

Key words: differential evolution algorithm, multi-static sonar, time difference of arrival, target localization

中图分类号:

TB 566

韦强强, 许林周, 韩东, 郭雨桐. 基于差分进化算法的多基地声纳目标定位[J]. 系统工程与电子技术, 2026, 48(6): 1819-1829.

Qiangqiang WEI, Linzhou XU, Dong HAN, Yutong GUO. Target localization for multi-static sonar based on differential evolution algorithm[J]. Systems Engineering and Electronics, 2026, 48(6): 1819-1829.

图/表 17

图1

图2

图3

图4

表1

表2

图5

图6

图7

图8

图9

图10

图11

图12

图13

表3

图14

参考文献 28

1	LUO J H, HAN Y, FAN L Y. Underwater acoustic target tracking: a review[J]. Sensors, 2018, 18 (1): 112. doi: 10.3390/s18010112
2	THUILLIER O, JOSSE N L, OLTEANU A L, et al. An improved two-phase heuristic for active multi-static sonar network configuration[J]. Expert Systems with Applications, 2024, 238, 121985. doi: 10.1016/j.eswa.2023.121985
3	HO K C. Bias reduction for an explicit solution of source localization using TDOA[J]. IEEE Trans. on Signal Processing, 2012, 60 (5): 2101- 2114. doi: 10.1109/TSP.2012.2187283
4	LIU Y, WANG Y M, CHEN C. Efficient underwater acoustical localization method based on TDOA with sensor position errors[J]. Journal of Marine Science and Engineering, 2023, 11 (4): 861.
5	CHEN D J, LI G J, FAN Y S. Hybrid positioning algorithm based on least squares and LM for 3D cluster networks[J]. Physical Communication, 2024, 66, 102400. doi: 10.1016/j.phycom.2024.102400
6	FAN C, WANG D, YANG B, et al. An algorithm for underwater target localization of multi-static sonar system with unknown signal propagation speed[J]. Acta Armamentarii, 2022, 43 (3): 637- 652.
7	WANG L, SHEN X H, KANG Y Z, et al. Least squares estimation performance for tdoa target localization in underwater acoustic sensor networks[J]. Acta Armamentarii, 2020, 41 (3): 542- 551.
8	HUANG B Q, XIE L H, YANG Z. TDOA-based source localization with distance-dependent noises[J]. IEEE Trans. on Wireless Communications, 2015, 14 (1): 468- 480. doi: 10.1109/TWC.2014.2351798
9	CHAN Y T, HO K C. A simple and efficient estimator for hyperbolic location[J]. IEEE Trans. on Signal Processing, 1994, 42 (8): 1905- 1915. doi: 10.1109/78.301830
10	YANG K, AN J P, BU X Y, et al. Constrained total least-squares location algorithm using time-difference-of-arrival measurements[J]. IEEE Trans. on Vehicular Technology, 2010, 59 (3): 1558- 1562. doi: 10.1109/TVT.2009.2037509
11	YANG T C, YU C Q, WANG T P, et al. A single observer location method under the scatter signals position disturbance situation: the constraint total least square method[J]. SCIENCE CHINA Information Sciences, 2011, 54 (1): 146- 152. doi: 10.1007/s11432-010-4129-z
12	ZHENG J, LUI K W K, SO H C. Accurate three-step algorithm for joint source position and propagation speed estimation[J]. Signal Processing, 2007, 87 (12): 3096- 3100. doi: 10.1016/j.sigpro.2007.06.014
13	WANG D, YIN J X, TANG T, et al. A two-step weighted least-squares method for joint estimation of source and sensor locations: a general framework[J]. Chinese Journal of Aeronautics, 2019, 32 (2): 417- 443. doi: 10.1016/j.cja.2018.12.027
14	XUE J, CHEN Y, HE F J. The constraint weighted least-squares algorithm of TDOA based on hierarchy in underwater sensor wireless network[J]. Chinese Journal of Sensors and Actuators, 2015, 28 (2): 239- 243.
15	LAKSHMI Y V, SINGH P, ABOUHAWASH M, et al. Improved chan algorithm based optimum UWB sensor node localization using hybrid particle swarm optimization[J]. IEEE Access, 2022, 10, 32546- 32565. doi: 10.1109/ACCESS.2022.3157719
16	RUI L, HO K C. Efficient closed-form estimators for multi-static sonar localization[J]. IEEE Trans. on Aerospace and Electronic Systems, 2015, 51 (1): 600- 614. doi: 10.1109/TAES.2014.140482
17	GOU Y N, WANG Y M, WANG Q. Applying simulated annealing algorithm to locating multi-static buoy[J]. Journal of Northwestern Poly-technical University, 2013, 31 (4): 607- 613.
18	尹宣紫, 黄志浩, 周子凌. 基于海洋捕食者算法的多基地声纳定位技术[C]//中国声学学会水声学分会学术会议, 2022: 295−298.
	YIN X Z, HUANG Z H, ZHOU Z L. Multi-base sonar localization technology based on marine predators algorithm [C]//Academic Conference of the Underwater Acoustics Branch of the Chinese Acoustical Society, 2022: 295−298.
19	STORN R, PRICE K. Differential evolution−a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11 (4): 341- 359. doi: 10.1023/A:1008202821328
20	DAS S, ABRAHAM A, CHAKRABORTY U K. Differential evolution using a neighborhood-based mutation operator[J]. IEEE Trans. on Evolutionary Computation, 2009, 13 (3): 526- 553. doi: 10.1109/TEVC.2008.2009457
21	CHEN M Y, FENG C C, CHENG R. MetaDE: evolving differential evolution by differential evolution[J]. IEEE Trans. on Evolutionary Computation, doi: 10.1109/TEVC.2025.3541.587
22	WU W M, PU W, WU J J, et al. A geometry and synchronization error decoupling and compensation approach for multi-static SAR imaging[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2024, 17, 15431- 15442. doi: 10.1109/JSTARS.2024.3439876
23	AN H Y, SHEN M X, WANG C D, et al. Multi-static synthetic aperture radar baseline design for 3-D imaging[C]//Proc. of the IGARSS IEEE International Geoscience and Remote Sensing Symposium, 2022: 2502−2505.
24	SUN Z C, REN H, YANG J Y, et al. Array arrangement design of multi-static sparse linear array SAR for 3-D imaging[C]//Proc. of the IEEE USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), 2022: 50−51.
25	何振宇, 毛亿, 杨扬, 等. 基于改进差分进化算法的GNSS无源多基地雷达海上目标定位方法[J]. 通信学报, 2025, 46 (2): 44- 58. doi: 10.11959/j.issn.1000-436x.2025024
	HE Z Y, MAO Y, YANG Y, et al. Maritime moving target localization method based on improved differential evolution with GNSS-based passive multi-static radar[J]. Journal on Communications, 2025, 46 (2): 44- 58. doi: 10.11959/j.issn.1000-436x.2025024
26	包子阳, 余继周, 杨杉. 智能优化算法及其MATLAB实例[M]. 3版. 北京: 电子工业出版社, 2021: 37−45.
	BAO Z Y, YU J Z, YANG S. Intelligent optimization algorithms and matlab implementation[M]. 3rd ed. Beijing: Publishing House of Electronics Industry, 2021: 37–45.
27	张春美. 差分进化算法理论与应用[M]. 北京: 北京理工大学出版社, 2014: 2−71.
	ZHANG C M. Theory and application of differential evolution algorithms [M]. Beijing: Beijing Institute of Technology Press, 2014: 2–71.
28	KARIN Z, PETRA W, RAINER L, et al. Parameter study for differential evolution using a power allocation problem including interference cancellation[C]//Proc. of the IEEE International Conference on Evolutionary Computation, 2006: 1857−1864.

最大迭代次数	种群数量$N$	缩放因子$F$	交叉概率${\mathrm{CR}}$
100	5	0.1 ~ 2（步进0.1）	0.05 ~ 0.95（步进0.05）
	10	0.1 ~ 2（步进0.1）	0.05 ~ 0.95（步进0.05）
	20	0.1 ~ 2（步进0.1）	0.05 ~ 0.95（步进0.05）
	50	0.1 ~ 2（步进0.1）	0.05 ~ 0.95（步进0.05）
	100	0.1 ~ 2（步进0.1）	0.05 ~ 0.95（步进0.05）

噪声水平	DE算法	SA算法	牛顿迭代算法
低噪声	13.43	14.85	9.05
中噪声	13.50	14.95	9.39
高噪声	13.64	15.14	9.26

[1]	谢欣辰, 高林, 魏平, 李万春. 基于到达时间差与频率差量测无偏转换的辐射源跟踪算法[J]. 系统工程与电子技术, 2026, 48(3): 751-757.
[2]	付留芳, 许林周, 周明, 董晓明, 寇祝. 基于二次优化的T-Rⁿ型多基地声纳部署方法[J]. 系统工程与电子技术, 2025, 47(5): 1600-1608.
[3]	王勇, 张博雅. 基于特征融合和定位增强的SAR图像舰船目标检测方法[J]. 系统工程与电子技术, 2025, 47(11): 3586-3597.
[4]	唐强, 邵高平, 孙明磊, 邵帅. 传感器位置误差下TDOA-DOA水下目标被动定位算法[J]. 系统工程与电子技术, 2024, 46(8): 2572-2580.
[5]	隆雨佟, 陈爱国, 史红权, 曾黎. 基于改进差分进化算法的跨平台武器目标分配方法[J]. 系统工程与电子技术, 2024, 46(3): 953-962.
[6]	李胜西, 李海阳, 何湘粤. 面向全球快速重访的限制性Walker星座设计方法[J]. 系统工程与电子技术, 2024, 46(12): 4149-4156.
[7]	汤建龙, 解佳龙, 陈弘凯. 无需先验测量误差的定位节点选择方法[J]. 系统工程与电子技术, 2024, 46(1): 35-41.
[8]	郑晶月, 吴佩仑, 陈家辉, 郭世盛, 崔国龙. 车载毫米波雷达多径假目标分析与消除方法[J]. 系统工程与电子技术, 2024, 46(1): 88-96.
[9]	张铠宇, 于昊天, 卢雨. 一种基于双站协同的时差频差定位方法[J]. 系统工程与电子技术, 2023, 45(9): 2698-2705.
[10]	何胜阳, 杜杰朋, 赵雅琴, 王宝莹, 赵亮, 吴龙文. 基于TDOA的无人机集群协同单目标定位[J]. 系统工程与电子技术, 2023, 45(1): 1-8.
[11]	谭目来, 丁达理, 谢磊, 丁维, 吕丞辉. 基于模糊专家系统与IDE算法的UCAV逃逸机动决策[J]. 系统工程与电子技术, 2022, 44(6): 1984-1993.
[12]	陈云翔, 饶益, 蔡忠义, 王泽洲. 基于改进相似性的装备部件剩余寿命预测及经济性储备策略[J]. 系统工程与电子技术, 2021, 43(9): 2688-2696.
[13]	吴文海, 郭晓峰, 周思羽, 高丽. 基于随机邻域策略和广义反向学习的自适应差分进化算法[J]. 系统工程与电子技术, 2021, 43(7): 1928-1942.
[14]	吴文海, 郭晓峰, 周思羽, 高丽. 改进差分进化算法求解武器目标分配问题[J]. 系统工程与电子技术, 2021, 43(4): 1012-1021.
[15]	魏蓝, 李威, 单家元. 稀薄流区的多弹协同编队构型生成策略设计[J]. 系统工程与电子技术, 2020, 42(8): 1812-1819.

基于差分进化算法的多基地声纳目标定位

Target localization for multi-static sonar based on differential evolution algorithm

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 17

参考文献 28

相关文章 15

编辑推荐

Metrics

本文评价

噪声水平	测量误差类别
噪声水平	${\sigma _p}$/m	${\sigma _c}$/（m/s）	${\sigma _t}$/ms
低噪声	10	5	10
中噪声	50	25	50
高噪声	100	50	100