一种基于加权多维标度分析的多个非相关源TDOA/FDOA协同定位方法

doi:10.7527/S1000-6893.2022.27105

Abstract

Abstract:

TDOA/FDOA localization is an important wireless positioning mechanism for moving emitters， and its location accuracy is greatly affected by measurement errors of TDOA/FDOA and prior measurement errors of sensor models （including sensor position and velocity）. To improve the localization performance under the condition of high-level measurement errors， a TDOA/FDOA cooperative localization method for multiple disjoint sources is proposed based on weighted multidimensional scaling analysis in this paper. The proposed method consists of two calculation stages： Stage-a and Stage-b. Specifically， in Stage-a， two groups of scalar product matrices in multidimensional scaling analysis are employed to form the positioning relationship， which is further used to yield the solutions for the locations of multiple disjoint sources and sensors by constructing a weighting matrix. In Stage-b， a constrained minimization model is established based on the intermediate variables introduced in multidimensional scaling analysis to determine the estimation errors in Stage-a. By solving this optimization problem， the expression for the localization errors in Stage-a are obtained， so as to refine the position and velocity estimates of the multiple disjoint sources as well as the sensors. In addition， the first-order error analysis is employed to prove that the proposed method can asymptotically reach the Cramér-Rao Bound （CRB） accuracy. Simulation results show that the new method outperforms the existing TDOA/FDOA positioning methods.

Key words: emitter localization, cooperative localization, Time Difference of Arrival (TDOA), Frequency Difference of Arrival (FDOA), weighted multidimensional scaling analysis, theoretical performance analysis

CLC Number:

V247

Ding WANG, Jiexin YIN, Xinguang ZHANG, Na’e ZHENG. A TDOA/FDOA cooperative localization method for multiple disjoint sources based on weighted multidimensional scaling analysis[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(7): 327105-327105.

Figures/Tables 13

Fig. 1

Table 1

Numerical value of sensor position and velocity

传感器序号	$x m (s)$ /m	$y m (s)$ /m	$z m (s)$ /m	$x ˙ m (s)$ /（m⋅s^-1）	$y ˙ m (s)$ /（m⋅s^-1）	$z ˙ m (s)$ /（m⋅s^-1）
1	2 400	1 800	1 300	-10	16	15
2	1 700	2 100	-2 200	10	-15	16
3	2 300	-1 900	1 600	-18	-10	18
4	-1 600	1 700	1 500	-10	10	-18
5	2 500	-1 600	-1 200	-10	18	15
6	-1 100	-1 400	2 400	18	-15	-16
7	-2 200	1 500	-2 500	15	-10	16

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Table 2

Table B1

Computational complexity of proposed method

步骤	各步骤计算量	总计算量
步骤a-1	$M (M + 1) N$	$12 M 4 N + 64 M 2 N 3 + 192 M 2 N 2 + 256 M N 3 + 104 M 3 N + 56 M N 2 + 342 M 2 N - 96 N 3 + 68 N 2 + 36 M 2 + 489 M N + 309 N + N O (8 (M - 1) 3) + 2 O ((6 M + 8 N) 3) + 2 N O (53) + O (8 N 3)$
步骤a-2	$(107 M + O (53)) N$
步骤a-3	$15 M 2 N$
步骤a-4	$128 M N 3 + 16 M N 2 + 64 N 2$
步骤a-5	$(12 M 4 + 438 M 2 + 225 M + 225 + O (53)) N$
步骤a-6	$16 M (M - 1) 2 N$
步骤a-7	$(16 (M - 1) 3 + 24 M 2 (M - 1) + 48 M (M - 1) 2 + O (8 (M - 1) 3)) N$
步骤a-8	$32 (M - 1) 2 N 3 + 128 (M - 1) N 3 + 96 M (M - 1) N 2 + 4 M (M - 1) N + (8 N + 6 M) (6 M + 2 (M - 1) N) + O ((6 M + 8 N) 3)$
步骤b-1	$32 (M - 1) 2 N 3 + 128 (M - 1) N 3 + 96 M (M - 1) N 2 + O ((6 M + 8 N) 3)$
步骤b-2	$24 N$
步骤b-3	$12 N$
步骤b-4	$2 (8 N + 6 M) 2 N + (8 N + 6 M) × (4 N 2 + 2 N) + 4 N 2 + O (8 N 3)$

Table B1

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定位方法	平均运行时间/s
本文方法	1.374 2
文献［27］方法	0.329 2
文献［31］方法	0.663 9
文献［34］方法	0.664 2
文献［35］方法	0.681 6
文献［13］方法	3.274 2

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A TDOA/FDOA cooperative localization method for multiple disjoint sources based on weighted multidimensional scaling analysis

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