联合时延-多普勒-角度的无源雷达目标定位凸优化算法

Convex Solution for Target Localization in Passive MIMO Radar Using Delay,Doppler and Angle Measurements

针对分布式多输入多输出雷达中联合时延-多普勒-角度测量的运动目标定位问题,提出了一种基于半正定松弛的凸优化定位算法,改善了测量误差较大时定位误差偏离克拉美罗界的阈值效应.首先,将定位问题表述为最大似然估计问题,通过引入辅助变量将定位问题转化为带约束的加权最小二乘优化问题,然后使用半正定松弛技术,转化为半正定规划凸问题,并采用内点法对该凸问题求解得到目标位置和速度估计.由于凸优化问题的局部最优解就是全局最优解,本文算法具有良好的全局收敛性.仿真结果表明,与现有算法相比,本文算法的定位误差逼近克拉美罗下界,在大测量误差水平下的定位精度和稳健性优于现有算法.

A convex-optimum localization algorithm based on semidefinite relaxation is proposed for moving target localization from time delay,Doppler shift and angle of arrival measurements in distributed multiple-input multipleoutput radar.This algorithm alleviates the threshold effect that the positioning error deviates from the Cramer-Rao lower bound(CRLB)when the measurement error is large.First,the localization problem is formulated as a maximum likelihood estimation problem,which is reformulated as a weighted least squares problem with constraints by introducing auxiliary variables and then a convex semidefinite programming(SDP)problem by performing semidefinite relaxation.The SDP problem is solved efficiently by using the interior-point method to obtain the target position and velocity estimates.Since the local optimal solution of the convex optimization problem is the global optimal solution,the proposed algorithm has good global convergence.Simulation results demonstrate that the proposed algorithm approaches the CRLB,and achieves higher localization accuracy and robustness than existing algorithms at relatively large measurement noise levels.