基于改进非洲秃鹫算法的TDOA-AOA定位

doi:10.13229/j.cnki.jdxbgxb.20230076

摘要/Abstract

摘要：

针对到达时间差定位（Time difference of arrival，TDOA）和到达角定位（Angle of arrival，AOA）联合定位，提出了基于准反射学习机制和并行机制改进的非洲秃鹫定位算法。改进的非洲秃鹫算法在对定位模型最大似然的适应度函数寻优和迭代过程中，引入准反射机制以丰富种群多样性和加快收敛速度，在一定程度上也平衡了探索和开发能力；引入并行机制，通过一个种群的最优个体指导另一种群，加快收敛速度，增强了寻优性能。实验结果看，将改进的非洲秃鹫算法与非洲秃鹫算法（AVOA）、改进的哈里斯鹰算法（IHHO）、混沌麻雀搜索优化算法（CSSOA）、鸽群优化算法（PIO）、疯狂自适应樽海鞘算法（CASSA）进行对比，在基准函数和定位模型的求解上，都表现出了更快的收敛速度、更准确的定位精度和更好的稳定性。

关键词: 信息处理技术, 到达时间差定位, 到达角定位, 非洲秃鹫算法, 准反射学习

Abstract:

For joint localization of time difference of arrival （TDOA） and angle of arrival （AOA）， an improved African vulture localization algorithm based on quasi reflective learning mechanism and parallel mechanism was proposed. The improved African vulture introduced a quasi reflection mechanism to enrich population diversity and speed up convergence in the process of searching for the maximum likelihood fitness function of the location model and in the iterative process， which also balanced the exploration and exploitation capabilities to a certain extent； The parallel mechanism was introduced to guide another population through the optimal individual of one population， which speeds up the convergence speed and enhances the optimization performance. From the results， the improved African Vulture algorithm is compared with AVOA， IHHO， CSSOA， PIO and CASSA， and shows faster convergence speed， more accurate positioning accuracy and better stability in solving the benchmark function and positioning model.

Key words: information processing technology, time difference of arrival, angle of arrival, african vultures optimization algorithm, quasi reflection

中图分类号:

TP277

肖剑,刘经纬,胡欣,齐小刚. 基于改进非洲秃鹫算法的TDOA-AOA定位[J]. 吉林大学学报(工学版), 2024, 54(12): 3558-3567.

Jian XIAO,Jing-wei LIU,Xin HU,Xiao-gang QI. TDOA⁃AOA location based on improved african vulture algorithm[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(12): 3558-3567.

图/表 10

图1

图2

表1

基准函数"

Functions	$D$	$R a n g e$
$F 1 = ∑ i = 1 n x i 2$	$100$	$[- 100,100] D$
$F 2 = ∑ i = 1 n x i - ∏ i = 1 n x i$	$100$	$[- 10,10] D$
$F 3 = ∑ i = 1 n (∑ j = 1 i x j) 2$	$30$	$[- 100,100] D$
$F 4 = m a x i {x i, 1 ≤ i ≤ n}$	$30$	$[- 100,100] D$
$F 5 = - 20 e (- 0.2 1 n ∑ i = 1 n x i 2) ???????? - e (1 n ∑ i = 1 n c o s (2 π x i) + 20 + e$	$10$	$[- 32,32] D$
$F 6 = 0.1 {s i n 2 (3 π x i) ????????? + ∑ i = 1 n - 1 (x i - 1) [1 + s i n 2 (3 π x i + 1)] ????????? + (x n - 1) [1 + s i n 2 (2 π x n)]} ?????????? + ∑ i = 1 n u (x i, 5,100,4)$	$100$	$[- 50,50] D$

表1

图3

表2

基准函数仿真结果"

函数	值	PQRAVOA	AVOA	IHHO	CSSOA	PIO	CASSA
$F 1$	Ave	0	7.763E-120	0	2.556E-228	6.673E-12	2.624E-13
$F 1$	Std	0	1.731E-119	0	0	1.481E-11	4.465E-13
$F 2$	Ave	2.074E-217	2.641E-60	4.058E-187	8.177E-106	1.479E-8	8.448E-6
$F 2$	Std	0	5.813E-60	0	1.698E-105	2.196E-8	1.842E-5
$F 3$	Ave	0	2.218E-76	1.937E-284	1.039E-165	2.045E-12	9.342E-9
$F 3$	Std	0	4.202E-76	0	0	2.132E-12	2.089E-8
$F 4$	Ave	1.915E-212	3.967E-60	1.953E-162	1.309E-111	6.588E-7	5.463E-10
$F 4$	Std	0	8.385E-60	4.445E-162	1.511E-111	1.369E-7	5.712E-10
$F 5$	Ave	3.801E-9	1.522E-3	8.922E-3	7.711E-5	7.202	13.606
$F 5$	Std	3.778E-9	1.191E-3	1.429E-2	8.332E-5	8.228	10.969
$F 6$	Ave	1.113E-11	4.541E-8	4.718E-5	7.469E-9	9.601E-3	2.232E-2
$F 6$	Std	1.003E-11	2.134E-8	4.652E-5	1.671E-8	1.285E-2	3.323E-2

表2

图4

图5

图6

图7

表3

不同距离噪声下的均方根误差对比"

$σ (m)$	RMSE
$σ (m)$	AVOA	PQRAVOA	CSSOA	IHHO	CASSA	PIO
0.1	0.040 5	0.011 9	0.016 3	0.066 2	0.235 3	0.029 3
0.2	0.058 7	0.022 6	0.025 8	0.079 2	0.241 9	0.042 8
0.3	0.073 1	0.035 1	0.036 9	0.085 8	0.247 2	0.061 6
0.4	0.083 6	0.046 7	0.049 2	0.093 9	0.248 3	0.075 5
0.5	0.092 2	0.055 1	0.061 2	0.108 7	0.284 8	0.092 9
0.6	0.100 4	0.064 2	0.073 2	0.113 4	0.299 3	0.103 4
0.7	0.111 1	0.076 5	0.080 6	0.123 1	0.275 4	0.114 1
0.8	0.119 1	0.088 8	0.097 2	0.138 5	0.305 9	0.127 1
0.9	0.124 2	0.099 2	0.103 5	0.147 6	0.301 1	0.131 7
1.0	0.131 9	0.108 5	0.117 8	0.158 2	0.288 1	0.148 9

表3

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