基于半正定松弛的到达频率差目标定位方法

doi:10.11959/j.issn.1000-0801.2024076

Abstract

Abstract:

The use of frequency measurements to achieve target positioning is characterized by low cost and high reliability.Using only frequency difference of arrival (FDOA) measurements, a precise localization method for static target position was proposed.To address the highly nonlinear of the established frequency measurement equation, it was transformed into a pseudo-linear equation in matrix form by introducing auxiliary variables.Then the non-convex weighted least squares (WLS) problem was relaxed into a semi-definite programming (SDP) problem by using the semi-definite relaxation (SDR) method, so as to further accurately estimate the position of unknown variables.Finally, the root mean square error (RMSE) of the proposed method was analyzed to verify its performance.The simulation results show that the performance of the adopted semi-definite relaxation method is able to reach the Cramer-Rao lower bound (CRLB) at lower Gaussian noise levels and the algorithm is highly robust to geometry.In addition, its RMSE performance is better than that of the two-stage weighted least square (TSWLS) method for a smaller number of sensors.

Key words: frequency measurement, frequency difference of arrival, semi-definite relaxation, semi-definite programming, static target positioning

CLC Number:

TN929.5

Xiaoting MAO, Xiaoping WU. Target localization method based on semi-definite relaxation with frequency difference of arrival[J]. Telecommunications Science, 2024, 40(3): 104-115.

Figures/Tables 10

方案	m	N_sd	$n_{i}^{sd}$
半正定松弛（SDR）	10	1	L₂

编号	${\dot{x}}_{i}$	${\dot{y}}_{i}$	编号	${\dot{x}}_{i}$	${\dot{y}}_{i}$
1	2	-13	9	2	11
2	-4	15	10	22	3
3	-3	-10	11	8	18
4	22	-13	12	1	20
5	24	-8	13	23	0
6	-1	10	14	-15	-22
7	7	10	15	8	7
8	-8	8	16	12	-24

References 25

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方案	m	n
第一阶段加权最小二乘（OSWLS）	N-1	L₁
第二阶段加权最小二乘（TSWLS）	L₁	k

编号	x_i	y_i	编号	x_i	y_i
1	-1 135	-1 872	9	-1 828	191
2	1 214	-1 843	10	-1 995	899
3	964	-643	11	475	-511
4	-336	-1 225	12	-824	-1 780
5	1 789	-1 458	13	803	1 572
6	-123	1 406	14	904	342
7	-1 013	-274	15	1 809	-557
8	1 977	1 711	16	-1 635	-52

编号	x^o	y^o	编号	x^o	y^o
1	400	300	5	-300	560
2	500	100	6	680	70
3	800	-100	7	-260	530

Target localization method based on semi-definite relaxation with frequency difference of arrival

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