基于蛇优化的单站机载无源定位算法

doi:10.12305/j.issn.1001-506X.2026.07.02

摘要/Abstract

摘要：

针对单站机载定位环境中定位精度有待提升的问题，提出一种基于元启发式蛇优化（snake optimizer，SO）算法的单站无源定位方法。该方法利用相位干涉仪测量目标相位差，构建代价函数，通过 SO 算法对代价函数进行寻优求解目标位置。为验证所提方法的有效性，对3种飞行模式下的机载定位模型进行仿真研究，并对比不同频率下的定位测试数据。实验结果表明，与经典智能算法相比，在低相位差误差场景中，SO 算法的定位精度提升约 1.4%；在相位差误差较大的场景中，定位精度提升约 2%；在不同频段目标辐射源的定位性能分析中，定位准确率提升约 2.3%。SO 算法能有效提高单站机载定位的精度，在复杂电磁环境下具有良好的适应性和应用价值。

关键词: 目标定位, 相位差定位, 蛇优化算法, 几何精度因子

Abstract:

Aiming at the problem that the positioning accuracy needs to be improved in the single station airborne positioning environment, a single station passive positioning method based on the meta-heuristic snake optimizer （SO） algorithm is proposed. This method uses a phase interferometer to measure the phase difference of the target, constructs a cost function, and optimizes the cost function to solve the target position through the SO algorithm. In order to verify the effectiveness of the proposed method, the airborne positioning models with three flight modes are simulated and the positioning test data at different frequencies are compared. Experimental results show that compared with the classical intelligent algorithms, the positioning accuracy of SO algorithm is improved by about 1.4% in the low phase difference error scenario. In scenarios with large phase difference errors, the positioning accuracy is improved by about 2%. In the analysis of the positioning performance of target radiation sources in different frequency bands, the positioning accuracy is improved by about 2.3%. SO algorithm can effectively improve the accuracy of single station airborne positioning, and has good adaptability and application value in complex electromagnetic environments.

Key words: target positioning, phase difference positioning, snake optimization （SO） algorithm, geometric dilution of precision

中图分类号:

TN 971

郭立民, 张逸飞, 马思达. 基于蛇优化的单站机载无源定位算法[J]. 系统工程与电子技术, 2026, 48(7): 2144-2152.

Limin GUO, Yifei ZHANG, Sida MA. Single station airborne passive positioning algorithm based on snake optimizer[J]. Systems Engineering and Electronics, 2026, 48(7): 2144-2152.

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参考文献 30

1	何维, 朱子越, 任彦, 等. 基于载波相位的RFID单站高精度定位算法[J]. 电子学报, 2022, 50 (3): 672- 680.
	HE W, ZHU Z Y, REN Y, et al. RFID single station high precision positioning algorithm based on carrier phase[J]. Acta Electronica Sinica, 2022, 50 (3): 672- 680.
2	李徽. 一种基于距离参数化CKF的单站无源定位方法[J]. 兵器装备工程学报, 2022, 50 (3): 672- 680.
	LI W. A single station passive location method based on distance parameterized CKF[J]. Journal of Weapon Equipment Engineering, 2022, 50 (3): 672- 680.
3	李泽, 王平, 田增山, 等. 基于终端侧的室内单站定位技术研究[J]. 电子学报, 2023, 51 (7): 1765- 1773.
	LI Z, WANG P, TIAN Z S, et al. Research on indoor single station positioning technology based on terminal side[J]. Acta Electronica Sinica, 2023, 51 (7): 1765- 1773.
4	JIANG W Y, XIA W, ZHONG S. Variable step-size normalized adaptive direct position determination by alternate iteration[C]//Proc. of the IEEE China Summit & International Conference on Signal and Information Processing, 2014: 772−776.
5	HU L P, LIANG X L, LI J, et al. Study on the method of determining formation configuration of aircraft swarms passive location[C]//Proc. of the IEEE 2nd International Conference on Computer and Communications, 2016: 1767−1771.
6	WANG J B, LUO X L. Research on airborne passive location based on extend Kalman filter with control inputs[C]//Proc. of the 3rd InternationalConference on Information Science and Control Engineering, 2016: 1389−1392.
7	JIANG B, LU A N, YOU M Y, et al. A single-observer passive location algorithm base on weighted least squares criterion[C]//Proc. of the IEEE 22nd International Conference on Communication Technology, 2022: 1750−1754.
8	夏雄, 杨阳, 胡飞. 基于改进霍夫变换的机载单站对多目标无源定位[J]. 电子信息对抗技术, 2021, 36 (3): 50- 53.
	XIA X, YANG Y, HU F. Multi-target passive location of airborne single station based on improved Hough transform[J]. Electronic Information Countermeasure Technology, 2021, 36 (3): 50- 53.
9	BHARNE P K, GULHANE V S, YEWALE S K. Data clustering algorithms based on swarm intelligence[C]//Proc. of the 3rd International Conference on Electronics Computer Technology, 2011.
10	ZHAO K L, LU T T, ZHANG H. An under-water wireless sensor network localization algorithm based on salp swarm optimization[C]//Proc. of the IEEE 3rd International Conference on Power, 2023: 232−237.
11	ARAFAT M Y, MOH S. Localization and clustering based on swarm intelligence in UAV networks for emergency communications[J]. IEEE Internet of Things Journal, 2019, 6 (5): 8958- 8976. doi: 10.1109/JIOT.2019.2925567
12	WAN Y S, XUE J C, QI H, et al. Research on microseismic source localization based on improved particle swarm optimization algorithm[C]//Proc. of the 4th International Conference on Artificial Intelligence, Robotics, and Communication, 2024: 713−716.
13	YANG F, WANG P X, ZHANG Y Z, et al. Survey of swarm intelligence optimization algorithms[C]//Proc. of the IEEE International Conference on Unmanned Systems, 2017: 544−549.
14	DU X P, CHENG L Z, LIU L F. A swarm intelligence algorithm for joint sparse recovery[J]. IEEE Signal Processing Letters, 2013, 20 (6): 611- 614. doi: 10.1109/LSP.2013.2260822
15	DONG X Z, WU Z R, CHEN L, et al. Study on distribution network failure positioning algorithm based on gaussian variation swarm-intelligence optimization algorithm[C]//Proc. of the China International Conference on Electricity Distribution , 2018: 157−161.
16	LV X W, LIU K H, HU P. Geometry influenceon GDOP in TOA and AOA positioning systems[C]//Proc. of the 2nd International Conference on Networks Security, Wireless Communications and Trusted Computing, 2010.
17	JIANG X H, LI N, GUO Y, et al. Sensing matrixoptimization for multi-target localization using compressed sensing in wireless sensor net-work[J]. China Communications, 2022, 19 (3): 230- 244. doi: 10.23919/JCC.2022.03.017
18	FAKHOURI H N, AWAYSHEH F M, ALAWADI S, et al. Four vector intelligent metaheuristic for data optimization[J]. Computing, 2024, 106 (7): 2321- 2359. doi: 10.1007/s00607-024-01287-w
19	KUO S Y, WU C H, CHEN C C, et al. A novel metaheuristic: fast jaguar algorithm[C]//Proc. of the IEEE International Conference on Systems, Man, and Cybernetics, 2021: 146−151.
20	HASHIM F A, HUSSIEN A G. Snake optimizer: a novel meta-heuristic optimization algorithm[J]. Knowledge-Based Systems, 2022, 242, 108320.
21	SONG B B, ZHU L, WANG C M, et al. Study on the application of intelligent optimization algorithm in the optimization of passive positioning network layout[C]//Proc. of the International Conference on Information Technology and Computer Application, 2019: 192−196.
22	ZHANG Y, LIU Y, SONG H L. Research on the application of improved salp swarm algorithm in time difference of arrival of passive location[C]//Proc. of the 21st International Symposium on Distributed Computing and Applications for Business Engineering and Science, 2022: 146−150.
23	ZHOU R H, SUN H M, LI H, et al. Time-difference-of-arrival location method of UAV swarms based on Chan-Taylor[C]//Proc. of the 3rd Inernational Conference on Unmanned Systems, 2020: 1161−1166.
24	WU J Y. An improved quantum-behaved particle swarm optimization method for solving constrained global optimization problems[C]//Proc. of the 15th International Symposium on Communications and Information Technologies, 2015: 157−160.
25	WANG H Q, JIANG J F, GUO X L, et al. Hypersonic vehicle reentry trajectory optimization based on particle swarm algorithm[C]//Proc. of the International Conference on Autonomous Unmanned Systems, 2024: 242−251.
26	COELLO C A C, PULIDO G T, LECHUGA M S. Handling multiple objectives with particle swarm optimization[J]. IEEE Trans. on Evolutionary Computation, 2004, 8 (3): 256- 279. doi: 10.1109/TEVC.2004.826067
27	RAO C Y, WANG Z L, SHAO P. A multi-strategy collaborative grey wolf optimization algorithm for UAV path planning[J]. Electronics, 2024, 13 (13): 2532. doi: 10.3390/electronics13132532
28	GOPI S, MOHAPATRA P. A modified grey wolf optimization algorithm to solve global optimization problems[J]. Opsearch, 2025, 62 (1): 337- 367. doi: 10.1007/s12597-024-00785-x
29	ZHANG M Y, LIU F, WANG Y J, et al. Mult UAV three-dimensional path planning based onimproved grey wolf optimization algorithm[C]//Proc. of the 43rd Chinese Control Conference, 2024: 2112−2117.
30	ZHANG C H, ZHOU Y, BI Y, et al. Aerial target motion feature selection based on improved grey wolf optimization algorithm[C]//Proc. of the 2nd International Conference on Algorithms, High Performance Computing and Artificial Intelligence, 2022: 154−159.

测试函数	坐标范围/km
$ {F_1}(x) = \displaystyle\sum\limits_{i = 1}^n {x_i^2} $	[−100, 100]
$ {F_2}(x) = \displaystyle\sum\limits_{i = 1}^n {\left\| {{x_i}} \right\|} + \displaystyle\prod\limits_{i = 1}^n {\left\| {{x_i}} \right\|} $	[−10, 10]
$ {F_3}(x) = \displaystyle\sum\limits_{i = 1}^n {{{\left( { \displaystyle\sum\limits_{j = 1}^i {{x_j}} } \right)}^2}} $	[−100, 100]
$ {F_4}(x) = \max \left\{ {\left\| {{x_i}} \right\|,1 \leqslant i \leqslant n} \right\} $	[−100, 100]
$ {F_5}(x) = \displaystyle\sum\limits_{i = 1}^{n - 1} {\left[ {100{{( {{x_{i + 1}} - x_i^2} )}^2} + {{\left( {{x_i} - 1} \right)}^2}} \right]} $	[−30, 30]
$ {F_6}(x) = \displaystyle\sum\limits_{i = 1}^n {{{\left( {\left[ {{x_i} + 0.5} \right]} \right)}^2}} $	[−100, 100]

频率/GHz	本文算法/%	GWO算法/%	PSO算法/%
2	97.7	96.1	85.1
6	91.4	90.3	71.5
10	89.6	88.5	63.3
14	80.9	83.4	58.6
16	78.5	70.2	56.8

频率/GHz	本文算法/%	GWO算法/%	PSO算法/%
2	93.8	90.3	80.2
6	91.2	85.4	65.5
10	88.4	80.5	61.2
14	79.3	75.8	52.5
16	75.1	69.7	48.3

频率/GHz	本文算法/%	GWO算法/%	PSO算法/%
2	95.5	93.2	85.3
6	92.5	88.4	69.6
10	89.3	85.8	61.5
14	80.7	79.2	55.2
16	75.6	74.9	50.6

[1]	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.
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[6]	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.
[7]	董爱, 夏芒, 李陟, 卓志敏. 空中分布式协同时差测量系统目标定位技术研究[J]. 系统工程与电子技术, 2020, 42(4): 799-805.
[8]	卢雨, 周正. 空基外辐射源定位系统的观测站航迹优化[J]. 系统工程与电子技术, 2020, 42(12): 2708-2715.
[9]	田强, 冯大政, 杨凡, 胡豪爽. 基于线性校正的TOA联合同步与定位算法[J]. 系统工程与电子技术, 2018, 40(2): 245-249.
[10]	孙扬, 郑娜娥, 李玉翔, 任修坤. 目标定位的分布式MIMO雷达资源分配算法[J]. 系统工程与电子技术, 2017, 39(2): 304-309.
[11]	雷文英，陈伯孝，杨明磊，朱伟. 基于TOA和TDOA的三维无源目标定位方法[J]. 系统工程与电子技术, 2014, 36(5): 816-823.
[12]	杨一，高社生，阎海峰. 临近空间伪卫星几何布局方案设计[J]. 系统工程与电子技术, 2014, 36(3): 532-538.
[13]	胡瑞贤，王彤，保铮. 扫描GMTI系统运动目标精确定位方法[J]. Journal of Systems Engineering and Electronics, 2013, 35(8): 1607-1614.
[14]	郭力，昂海松，郑祥明. 基于单目视觉的微型飞行器移动目标定位方法[J]. Journal of Systems Engineering and Electronics, 2012, 34(5): 996-1000.
[15]	雷雨, 冯新喜, 朱灿彬, 李彬彬. 2D雷达组网几何定位融合算法[J]. Journal of Systems Engineering and Electronics, 2011, 33(5): 1151-.