基于目标群拓扑特征的飞行器集群相对定位

doi:10.12305/j.issn.1001-506X.2025.11.28

Abstract

Abstract:

High-precision positioning of aircraft clusters is a necessary prerequisite for executing cooperative tasks. Aiming at the scenarios of multi target collaborative detection where the Global Navigation Satellite System (GNSS) is denied and environmental feature information is limited, a cooperative positioning method based on the topological features of target groups is proposed. This method uses only the distance measurements from the data link within the cluster and the multi target detection information. A distance-measurement polyhedron is constructed using multidimensional scaling (MDS), and target association is performed based on the three-dimensional topological features of the target group. A relative positioning optimization model is then established. The optimal solution for the polyhedron’s attitude is obtained by using an improved particle swarm optimization (PSO) algorithm with a compression factor. Simulation results demonstrate that high relative positioning accuracy of the cluster can be achieved. Combined with the inertial navigation system (INS) position output, the absolute positioning accuracy of the aircraft cluster is also improved.

Key words: relative positioning, target association, multidimensional scaling (MDS), particle swarm optimization (PSO)

CLC Number:

TN 96

Xingang MOU, Wenkai PENG, Xujun GUAN, Wenxing FU, Mingrui HAO. Relative positioning of aircraft cluster based on topological features of target group[J]. Systems Engineering and Electronics, 2025, 47(11): 3816-3825.

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References 30

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误差项	$\sigma _{\text{yaw }}/(^\circ) $	$\sigma _{\text{pitch}}/(^\circ) $	${\sigma _{\text{range}}}/{\text{m}}$	${\sigma _{{\theta}}}/(^\circ) $	${\sigma _{\phi}} /(^\circ) $	${\sigma _{{\text{dis}}}}/{\mathrm{m}}$
标准差	0.12	0.08	20	0.50	0.50	50

编号	1	2	3	4	5	6	7
1	0.91	0.53	0.72	0.42	0.47	0.56	0.68
2	0.57	0.92	0.54	0.63	0.42	0.48	0.54
3	0.58	0.33	0.91	0.21	0.43	0.50	0.77
4	0.58	0.66	0.35	0.92	0.36	0.46	0.41
5	0.39	0.30	0.53	0.30	0.88	0.70	0.60
6	0.38	0.35	0.44	0.33	0.45	0.81	0.56
7	0.62	0.50	0.85	0.41	0.72	0.64	0.94

视角1下的目标编号	视角2下的关联对象/关联概率
1	1/0.56，4/0.44
2	2/1.00
3	3/0.54，7/0.46
4	4/1.00
5	5/0.56，6/0.44
6	6/1.00
7	3/0.34，5/0.29，7/0.37

算法	${{\overline X_{\text{a}}}} {\text{/m}}$	${S_{\text{a}}}{\text{/m}}$	${{\overline X_{\text{b}}}} $/次	${S_{\text{b}}}$/次	${{\overline X_{\text{c}}}}/ {\text{s}}$	${S_{\text{c}}}/{\text{s}}$
基础PSO	4 171.996	4 624.603	66.780	24.992	0.359	0.134
标准PSO	2 728.829	6 376.173	178.070	31.148	0.954	0.165
压缩因子PSO	1 756.769	4 646.954	120.820	20.487	0.638	0.110
自适应惯性权重的混合PSO	2 569.188	5 966.492	152.740	23.087	0.818	0.122
动态调整惯性权重的PSO	1 798.137	5 259.375	189.900	28.512	1.082	0.162

算法	${{\overline X_{\text{a}}}} /{\text{m}}$	${S_{\text{a}}}/{\text{m}}$	${{\overline X_{\text{b}}}} /次$	${S_{\text{b}}}$/次	${{\overline X_{\text{c}}}} /{\text{s}}$	${S_{\text{c}}}/{\text{s}}$
基础PSO	595.867	396.302	66.475	21.560	0.336	0.128
标准PSO	0.000	0.000	182.170	4.638	0.910	0.115
压缩因子PSO	0.000	0.000	96.395	4.312	0.528	0.077
自适应惯性权重的混合PSO	4.692	57.738	152.115	5.813	0.765	0.111
动态调整惯性权重的PSO	16.905	161.072	196.875	20.046	1.055	0.164

Relative positioning of aircraft cluster based on topological features of target group

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对象	$x$向/km	$y$向/km	$z$向/km
飞行器	[0，5]	[0，5]	[5，10]
目标	[30，35]	[30，35]	[5，10]

参数	分布距离/m	${l_{\text{p}}}$/m
参数	分布距离/m	2500	5000	7500	10000
${l_{\mathrm{t}}}$/m	2500	[1.909，1.847，1.975]	[0.984，0.829，0.947]	[0.604，0.614，0.631]	[0.384，0.376，0.385]
	5000	[2.183，1.981，1.908]	[1.036，0.940，0.959]	[0.659，0.572，0.676]	[0.434，0.405，0.384]
	7500	[2.275，1.800，2.248]	[0.948，0.923，0.970]	[0.591，0.583，0.597]	[0.442，0.398，0.439]
	10000	[2.035，1.726，1.956]	[0.881，0.801，0.869]	[0.649，0.601，0.598]	[0.395，0.367，0.408]

节点	$\Delta x_i^{{{\mathrm{I}}}}$	$ \Delta \tilde x_i^{\mathrm{I}} $	$\Delta y_i^{\mathrm{I}}$	$\Delta \tilde y_i^{\mathrm{I}}$	$\Delta z_i^{\mathrm{H}}$	$ \Delta \tilde z_i^{\mathrm{H}} $
1	−43.650	114.609	1015.283	−87.193	−34.083	−7.096
2	676.378	128.276	−958.789	−81.230	−11.314	−6.544
3	−237.013	125.531	−858.570	−87.963	2.934	13.944
4	700.412	128.895	887.410	−81.721	9.436	−3.688
5	−127.239	121.779	−1123.647	−81.727	28.650	−15.505
6	−232.733	117.065	528.499	−89.980	−7.150	7.363

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节点数量	5	6	7	8
精度提升倍数	3.871	4.064	4.331	4.585