UAV swarm formation recognition algorithm based on multi-scale complex networks

doi:10.11772/j.issn.1001-9081.2025030362

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (3): 1004-1010.DOI: 10.11772/j.issn.1001-9081.2025030362

• Frontier and comprehensive applications •

UAV swarm formation recognition algorithm based on multi-scale complex networks

Tingquan DENG¹(), Yuling LI¹, Yonghang REN¹, Tian XIA¹, Kunfu WANG², Shengchun WANG²

^1.School of Mathematical Sciences，Harbin Engineering University，Harbin Heilongjiang 150001，China
^2.Systems Engineering Research Institute，China State Shipbuilding Corporation Limited，Beijing 100094，China

Received:2025-04-07 Revised:2025-07-03 Accepted:2025-07-04 Online:2025-08-13 Published:2026-03-10
Contact: Tingquan DENG
About author:LI Yuling， born in 1999， M. S. candidate. His research interests include data mining， machine learning.
REN Yonghang， born in 2000， M. S. candidate. His research interests include multi-objective optimization.
XIA Tian， born in 1999， M. S. candidate. His research interests include deep learning， artificial intelligence.
WANG Kunfu， born in 1986， Ph. D.， senior engineer. His research interests include computer information.
WANG Shengchun， born in 1991， Ph. D.， engineer. His research interests include computer graphics， image processing， high-performance computing.
Supported by:
National Natural Science Foundation of China(12171115);National Defense Basic Research Program of State Administration of Science, Technology and Industry for National Defence(JCKY2021206B056)

基于多尺度复杂网络的无人机集群队形识别算法

邓廷权¹(), 李予凌¹, 任泳行¹, 夏天¹, 王坤福², 王盛春²

^1.哈尔滨工程大学数学科学学院，哈尔滨 150001
^2.中国船舶集团有限公司系统工程研究院，北京 100094

通讯作者: 邓廷权
作者简介:李予凌（1999—），男，四川成都人，硕士研究生，主要研究方向：数据挖掘、机器学习
任泳行（2000—），男，重庆人，硕士研究生，主要研究方向：多目标优化
夏天（1999—），男，山东济南人，硕士研究生，主要研究方向：深度学习、人工智能
王坤福（1986—），男，山东青岛人，高级工程师，博士，主要研究方向：计算机信息
王盛春（1991—），男，陕西延安人，工程师，博士，主要研究方向：计算机图形学、图像处理、高性能计算。
基金资助:
国家自然科学基金资助项目(12171115);国防科技工业局国防基础研究计划项目(JCKY2021206B056)

Abstract

Abstract:

When dealing with incoming Unmanned Aerial Vehicles （UAVs）， it is crucial to recognize the formation of enemy UAVs quickly and accurately， in order to analyze and judge enemies’ combat intentions and formulate effective countermeasures. Therefore， a UAV swarm formation recognition algorithm based on multi-scale complex networks was proposed. Firstly， an adaptive threshold method was established to construct multi-scale complex networks using the UAV swarm formation， and the combination of eigenvalues corresponding to the adjacency matrices of these complex networks was selected to form a shape signature. Then， by introducing Hellinger distance to measure the difference between the shape signature of the formation to be recognized and the standard formation， so as to obtain the recognition results. Simulation results show that compared with the algorithm of obtaining multi-scale complex networks with hard thresholds， the proposed algorithm has better adaptability and robustness， has a higher recognition rate even when the target information is heavily corrupted， and has fewer parameters and lower time complexity.

Key words: multi-scale complex network, formation recognition, spectral graph theory, Hellinger distance, Unmanned Aerial Vehicle (UAV)

摘要：

在面对来袭无人机（UAV）时，快速准确地检测识别出敌方UAV的编队队形对于分析判断敌方的作战意图和制定有效的反制措施至关重要。因此，提出基于多尺度复杂网络的UAV集群队形识别算法。首先，建立自适应阈值方法将UAV集群队形构建为多尺度复杂网络，选择这些复杂网络对应的邻接矩阵的特征值组合，形成形状签名；其次，引入Hellinger距离度量待识别队形与标准队形的形状签名间的差异性，从而得到识别结果。仿真结果表明，与通过硬阈值得到多尺度复杂网络的算法相比，所提算法具有较好的适应性和鲁棒性，即使在目标信息受污染较严重时也具有较高的识别率，且具有较少的参数和较低的时间复杂度。

关键词: 多尺度复杂网络, 队形识别, 谱图理论, Hellinger距离, 无人机

CLC Number:

TP391

Tingquan DENG, Yuling LI, Yonghang REN, Tian XIA, Kunfu WANG, Shengchun WANG. UAV swarm formation recognition algorithm based on multi-scale complex networks[J]. Journal of Computer Applications, 2026, 46(3): 1004-1010.

邓廷权, 李予凌, 任泳行, 夏天, 王坤福, 王盛春. 基于多尺度复杂网络的无人机集群队形识别算法[J]. 《计算机应用》唯一官方网站, 2026, 46(3): 1004-1010.

Figures/Tables 9

Fig. 1 Multi-scale complex networks of cross-shaped formation under different soft threshold ranges

Fig. 2 Comparison of three formations’ shape signatures

Tab. 1 Similarity measurements of three formation templates

度量方法	队形	十字形	一字形	三叉形
Hellinger距离	十字形	0.000 0	0.079 3	0.076 3
	一字形	0.079 3	0.000 0	0.105 5
	三叉形	0.076 3	0.105 5	0.000 0
Pearson 相关系数	十字形	0.000 0	0.018 7	0.007 0
	一字形	0.018 7	0.000 0	0.019 9
	三叉形	0.007 0	0.019 9	0.000 0
余弦相似度	十字形	0.000 0	0.011 3	0.006 9
	一字形	0.011 3	0.000 0	0.014 3
	三叉形	0.006 9	0.014 3	0.000 0
欧氏距离	十字形	0.000 0	0.026 5	0.024 7
	一字形	0.026 5	0.000 0	0.032 4
	三叉形	0.024 7	0.032 4	0.000 0

Tab. 2 Time complexity corresponding to different values of n

顶点数n	时间复杂度
$n ≤ 50$	O（10³）
$50 < n ≤ 200$	O（4×10⁴）
$200 < n ≤ 1 000$	O（10⁶）
$n > 1 000$	O（n²）

Tab. 2 Time complexity corresponding to different values of n

顶点数n	时间复杂度
$n ≤ 50$	O（10³）
$50 < n ≤ 200$	O（4×10⁴）
$200 < n ≤ 1 000$	O（10⁶）
$n > 1 000$	O（n²）

Fig. 3 Five standard formations and their corresponding shape signatures

Tab. 3 Impact of nλand Δ on accuracy

$n λ$	Δ	不同队形的准确率/%
$n λ$	Δ	十字形	一字形	菱形	三叉形	V形
4	0.02	100.00	100.00	8.33	95.00	100.00
	0.05	100.00	100.00	3.33	88.33	93.33
	0.10	100.00	100.00	3.33	85.00	91.67
	0.20	100.00	100.00	6.67	58.33	35.00
6	0.02	100.00	100.00	8.33	93.33	100.00
	0.05	100.00	100.00	3.33	86.67	100.00
	0.10	100.00	100.00	0.00	85.00	95.00
	0.20	100.00	100.00	10.00	58.33	58.33
8	0.02	100.00	100.00	18.33	93.33	100.00
	0.05	100.00	100.00	5.00	91.67	100.00
	0.10	100.00	100.00	5.00	88.33	98.33
	0.20	100.00	100.00	18.33	58.33	66.67

Tab. 3 Impact of nλand Δ on accuracy

$n λ$	Δ	不同队形的准确率/%
$n λ$	Δ	十字形	一字形	菱形	三叉形	V形
4	0.02	100.00	100.00	8.33	95.00	100.00
	0.05	100.00	100.00	3.33	88.33	93.33
	0.10	100.00	100.00	3.33	85.00	91.67
	0.20	100.00	100.00	6.67	58.33	35.00
6	0.02	100.00	100.00	8.33	93.33	100.00
	0.05	100.00	100.00	3.33	86.67	100.00
	0.10	100.00	100.00	0.00	85.00	95.00
	0.20	100.00	100.00	10.00	58.33	58.33
8	0.02	100.00	100.00	18.33	93.33	100.00
	0.05	100.00	100.00	5.00	91.67	100.00
	0.10	100.00	100.00	5.00	88.33	98.33
	0.20	100.00	100.00	18.33	58.33	66.67

Tab. 4 Impact of nλ and nΔ on accuracy

n_λ	n_Δ	不同队形下的准确率/%
n_λ	n_Δ	十字形	一字形	菱形	三叉形	V形
4	6	100.00	100.00	25.00	86.67	51.67
	8	100.00	100.00	8.33	68.33	60.00
	10	100.00	100.00	73.33	71.67	93.33
6	6	100.00	100.00	35.00	93.33	60.00
	8	100.00	100.00	8.33	75.00	75.00
	10	100.00	100.00	81.67	71.67	96.67
8	6	100.00	100.00	40.00	93.33	65.00
	8	100.00	100.00	11.67	71.67	78.33
	10	100.00	100.00	88.33	73.33	96.67

Fig. 4 Comparison of five formations before and after adding noise

Tab. 5 Recognition accuracies of five formations under different noise intensities

强度	队形	不同方法的识别准确率/%
强度	队形	自适应阈值	硬阈值	Hough变换	SC
0.003	十字形	100.00	100.00	100.00	100.00
	一字形	100.00	100.00	100.00	100.00
	菱形	96.67	13.33	100.00	100.00
	三叉形	100.00	100.00	85.00	95.00
	V形	100.00	100.00	100.00	100.00
0.004	十字形	100.00	100.00	100.00	100.00
	一字形	100.00	100.00	100.00	98.33
	菱形	96.67	46.67	100.00	93.33
	三叉形	85.00	90.00	86.67	91.67
	V形	100.00	100.00	98.33	95.00
0.005	十字形	100.00	100.00	98.33	100.00
	一字形	100.00	100.00	100.00	100.00
	菱形	88.33	18.33	76.67	86.67
	三叉形	93.33	85.00	91.67	83.33
	V形	96.70	100.00	90.00	88.33

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UAV swarm formation recognition algorithm based on multi-scale complex networks

基于多尺度复杂网络的无人机集群队形识别算法

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