基于改进非洲秃鹫算法的TDOA-AOA定位

doi:10.13229/j.cnki.jdxbgxb.20230076

Abstract

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

CLC Number:

TP277

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.

Figures/Tables 10

Fig.1

Fig.2

Table 1

Benchmark Functions"

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

Table 1

Fig.3

Table 2

Results of benchmark functions"

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

Table 2

Fig.4

Fig.5

Fig.6

Fig.7

Table 3

Comparison of root mean square error under different distance noise standard deviation"

$σ (m)$	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

Table 3

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TDOA⁃AOA location based on improved african vulture algorithm

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