利用高斯牛顿迭代的时频差无源定位算法

doi:10.19665/j.issn1001-2400.2023.01.003

摘要/Abstract

摘要：

针对传统高斯牛顿迭代法在时差-频差定位中因迭代初始值不准而易出现的不收敛问题,提出一种基于约束加权最小二乘(CWLS)的高斯牛顿迭代定位算法。该算法首先将定位问题中关于目标位置、速度的时差-频差非线性定位方程转化为伪线性方程,分步估计目标位置、速度初始值;为实现初始值的精确估计,将目标位置与辅助变量等式约束关系松弛为二阶锥约束(SOCP)条件;引入随机鲁棒最小二乘(SRLS)构建新的线性关系,当新线性关系的最小二乘解不满足二阶锥约束条件时,使用半定规划(SDP)技术求解目标位置的估计解,通过获得的目标位置来对目标速度进行求解;获得目标参数估计初始值后,建立时差-频差定位系统下关于目标位置与速度的高斯牛顿迭代方程,利用高斯牛顿迭代对目标参数进行寻优求解,该迭代过程不需要引入辅助参数,可以直接得到目标参数。仿真实验表明,所提算法对近场目标与远场目标均有很好的定位效果,较已有经典两步加权算法,其鲁棒性好、定位精度高。同时,仿真结果表明了高斯牛顿迭代方程时对初始值优化的必要性。

关键词: 无源定位, 到达时间差, 到达频率差, 高斯牛顿迭代, 克拉美罗下界

Abstract:

To address the non-convergence problem of the traditional Gauss-Newton iterative method in time difference of arrival (TDOA) and frequency difference of arrival (FDOA) location due to the inaccurate iterative initial value,a Gauss-Newton iterative algorithm based on the constrained weighted least square (CWLS) is proposed.First,the nonlinear positioning equation in the positioning problem is transformed into a set of pseudo-linear equations about the target position and velocity.Initial values of the target position and velocity are estimated step by step.In order to realize the accurate estimation of the initial value,the equality constraint relationship between the target position and the auxiliary variable are relaxed to the second-order cone programming (SOCP) condition.The stochastic robust least square (SRLS) is introduced to construct a new linear relation.When the weighted least square solution does not meet the SOCP condition,the semi-definite programming (SDP) is used to solve the estimated solution of the target position.The target velocity is solved by the obtained target position.After obtaining the initial values of the target parameters,the Gaussian Newton iterative equations for the target position and velocity in the TDOA-FDOA localization system are established.Target parameters are solved by the Gaussian Newton iterative process,which does not require the introduction of auxiliary parameters and can directly obtain the target parameters.Simulation experiments show that the proposed algorithm has a good localization effect on both near-field and far-field targets,and that its robustness and high localization accuracy are better than those of the existing classical two-stage weighted algorithm.At the same time,simulation results show the necessity of optimizing the initial values when the Newton iterative equations are used.

Key words: passive localization, time difference of arrival, frequency difference of arrival, gauss-newton iteration, Cramér-Rao lower bound

中图分类号:

TN911

汤建龙, 解佳龙, 薛成均. 利用高斯牛顿迭代的时频差无源定位算法[J]. 西安电子科技大学学报, 2023, 50(1): 19-28.

TANG Jianlong, XIE Jialong, XUE Chengjun. TDOA-FDOA passive location algorithm using gauss-newton iteration[J]. Journal of Xidian University, 2023, 50(1): 19-28.

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坐标	x/m	y/m	z/m	x_v/(m·s^-1)	y_v/(m·s^-1)	z_v/(m·s^-1)
观测站1	300	100	150	30	20	20
观测站2	400	150	100	-30	10	20
观测站3	300	500	200	10	-20	10
观测站4	350	200	100	10	20	30
观测站5	-100	-100	-100	-20	20	20

算法	算法执行时间/ms
TSWLS^[8]	0.258
改进的TSWLS算法^[19]	0.293
改进的非完全约束算法^[20]	0.645
SDR^[9]	376.637
文中算法	122.589